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In string theory, the K-theory classification refers to a conjectured application of K-theory (in abstract algebra and algebraic topology) to superstrings, to classify the allowed Ramond-Ramond field strengths as well as the charges of stable D-branes.

In condensed matter physics K-theory has also found important applications, specially in the topological classification of topological insulators, superconductors and stable Fermi Surfaces (Template:Harvtxt, Template:Harvtxt).

History

This conjecture, applied to D-brane charges, was first proposed by Template:Harvtxt. It was popularized by Template:Harvtxt who demonstrated that in type IIB string theory arises naturally from Ashoke Sen's realization of arbitrary D-brane configurations as stacks of D9 and anti-D9-branes after tachyon condensation.

Such stacks of branes are inconsistent in a non-torsion Neveu-Schwarz (NS) 3-form background, which, as was highlighted by Template:Harvtxt, complicates the extension of the K-theory classification to such cases. Template:Harvtxt suggested a solution to this problem: D-branes are in general classified by a twisted K-theory, that had earlier been defined by Template:Harvtxt.

Applications

41 yr old Vehicle Painter Stephan from Oshawa, likes to spend some time legos, property developers in singapore and cake decorating. Was exceptionally stimulated after gonna Cistercian Abbey of Fontenay.

my page: http://www.everyanswers.com/78922/singapore-property-launch The K-theory classification of D-branes has had numerous applications. For example, Template:Harvtxt used it to argue that there are eight species of orientifold one-plane. Template:Harvtxt applied the K-theory classification to derive new consistency conditions for flux compactifications. K-theory has also been used to conjecture a formula for the topologies of T-dual manifolds by Template:Harvtxt. Recently K-theory has been conjectured to classify the spinors in compactifications on generalized complex manifolds.

Open problems

Despite these successes, RR fluxes are not quite classified by K-theory. Template:Harvtxt argued that the K-theory classification is incompatible with S-duality in IIB string theory.

In addition, if one attempts to classify fluxes on a compact ten-dimensional spacetime, then a complication arises due to the self-duality of the RR fluxes. The duality uses the Hodge star, which depends on the metric and so is continuously valued and in particular is generically irrational. Thus not all of the RR fluxes, which are interpreted as the Chern characters in K-theory, can be rational. However Chern characters are always rational, and so the K-theory classification must be replaced. One needs to choose a half of the fluxes to quantize, or a polarization in the geometric quantization-inspired language of Diaconescu, Moore, and Witten and later of Template:Harvtxt. Alternately one may use the K-theory of a 9-dimensional time slice as has been done by Template:Harvtxt.

K-theory classification of RR fluxes

In the classical limit of type II string theory, which is type II supergravity, the Ramond-Ramond field strengths are differential forms. In the quantum theory the well-definedness of the partition functions of D-branes implies that the RR field strengths obey Dirac quantization conditions when spacetime is compact, or when a spatial slice is compact and one considers only the (magnetic) components of the field strength which lie along the spatial directions. This led twentieth century physicists to classify RR field strengths using cohomology with integral coefficients.

However some authors have argued that the cohomology of spacetime with integral coefficients is too big. For example, in the presence of Neveu-Schwarz H-flux or non-spin cycles some RR fluxes dictate the presence of D-branes. In the former case this is a consequence of the supergravity equation of motion which states that the product of a RR flux with the NS 3-form is a D-brane charge density. Thus the set of topologically distinct RR field strengths that can exist in brane-free configurations is only a subset of the cohomology with integral coefficients.

This subset is still too big, because some of these classes are related by large gauge transformations. In QED there are large gauge transformations which add integral multiples of two pi to Wilson loops. The p-form potentials in type II supergravity theories also enjoy these large gauge transformations, but due to the presence of Chern-Simons terms in the supergravity actions these large gauge transformations transform not only the p-form potentials but also simultaneously the (p+3)-form field strengths. Thus to obtain the space of inequivalent field strengths from the forementioned subset of integral cohomology we must quotient by these large gauge transformations.

The Atiyah-Hirzebruch spectral sequence constructs twisted K-theory, with a twist given by the NS 3-form field strength, as a quotient of a subset of the cohomology with integral coefficients. In the classical limit, which corresponds to working with rational coefficients, this is precisely the quotient of a subset described above in supergravity. The quantum corrections come from torsion classes and contain mod 2 torsion corrections due to the Freed-Witten anomaly.

Thus twisted K-theory classifies the subset of RR field strengths that can exist in the absence of D-branes quotiented by large gauge transformations. Daniel Freed has attempted to extend this classification to include also the RR potentials using differential K-theory.

K-theory classification of D-branes

K-theory classifies D-branes in noncompact spacetimes, intuitively in spacetimes in which we are not concerned about the flux sourced by the brane having nowhere to go. While the K-theory of a 10d spacetime classifies D-branes as subsets of that spacetime, if the spacetime is the product of time and a fixed 9-manifold then K-theory also classifies the conserved D-brane charges on each 9-dimensional spatial slice. While we were required to forget about RR potentials to obtain the K-theory classification of RR field strengths, we are required to forget about RR field strengths to obtain the K-theory classification of D-branes.

K-theory charge versus BPS charge

As has been stressed by Petr Hořava, the K-theory classification of D-branes is independent of, and in some ways stronger than, the classification of BPS states. K-theory appears to classify stable D-branes missed by supersymmetry based classifications.

For example, D-branes with torsion charges, that is with charges in the order N cyclic group $Z_{N}$ , attract each other and so can never be BPS. In fact, N such branes can decay, whereas no superposition of branes that satisfy a Bogomolny bound may ever decay. However the charge of such branes is conserved modulo N, and this is captured by the K-theory classification but not by a BPS classification. Such torsion branes have been applied, for example, to model Douglas-Shenker strings in supersymmetric U(N) gauge theories.

K-theory from tachyon condensation

Ashoke Sen has conjectured that, in the absence of a topologically nontrivial NS 3-form flux, all IIB brane configurations can be obtained from stacks of spacefilling D9 and anti D9 branes via tachyon condensation. The topology of the resulting branes is encoded in the topology of the gauge bundle on the stack of the spacefilling branes. The topology of the gauge bundle of a stack of D9s and anti D9s can be decomposed into a gauge bundle on the D9's and another bundle on the anti D9's. Tachyon condensation transforms such a pair of bundles to another pair in which the same bundle is direct summed with each component in the pair. Thus the tachyon condensation invariant quantity, that is, the charge which is conserved by the tachyon condensation process, is not a pair of bundles but rather the equivalence class of a pair of bundles under direct sums of the same bundle on both sides of the pair. This is precisely the usual construction of topological K-theory. Thus the gauge bundles on stacks of D9's and anti-D9's are classified by topological K-theory. If Sen's conjecture is right, all D-brane configurations in type IIB are then classified by K-theory. Petr Horava has extended this conjecture to type IIA using D8-branes.

Twisted K-theory from MMS instantons

While the tachyon condensation picture of the K-theory classification classifies D-branes as subsets of a 10-dimensional spacetime with no NS 3-form flux, the Maldacena, Moore, Seiberg picture classifies stable D-branes with finite mass as subsets of a 9-dimensional spatial slice of spacetime.

The central observation is that D-branes are not classified by integral homology because Dp-branes wrapping certain cycles suffer from a Freed-Witten anomaly, which is cancelled by the insertion of D(p-2)-branes and sometimes D(p-4)-branes that end on the afflicted Dp-brane. These inserted branes may either continue to infinity, in which case the composite object has an infinite mass, or else they may end on an anti-Dp-brane, in which case the total Dp-brane charge is zero. In either case, one may wish to remove the anomalous Dp-branes from the spectrum, leaving only a subset of the original integral cohomology.

The inserted branes are unstable. To see this, imagine that they extend in time away (into the past) from the anomalous brane. This corresponds to a process in which the inserted branes decay via a Dp-brane that forms, wraps the forementioned cycle and then disappears. MMS^[1] refer to this process as an instanton, although really it need not be instantonic.

The conserved charges are thus the nonanomolous subset quotiented by the unstable insertions. This is precisely the Atiyah-Hirzebruch spectral sequence construction of twisted K-theory as a set.

Reconciling twisted K-theory and S-duality

Diaconescu, Moore, and Witten have pointed out that the twisted K-theory classification is not compatible with the S-duality covariance of type IIB string theory. For example, consider the constraint on the Ramond-Ramond 3-form field strength G₃ in the Atiyah-Hirzebruch spectral sequence (AHSS):

d_{3} G_{3} = S q^{3} G_{3} + H \cup G_{3} = G_{3} \cup G_{3} + H \cup G_{3} = 0

where d₃=Sq³+H is the first nontrivial differential in the AHSS, Sq³ is the third Steenrod square and the last equality follows from the fact that the nth Steenrod square acting on any n-form x is x $\cup$ x.

The above equation is not invariant under S-duality, which exchanges G₃ and H. Instead Diaconescu, Moore, and Witten have proposed the following S-duality covariant extension

G_{3} \cup G_{3} + H \cup G_{3} + H \cup H = P

where P is an unknown characteristic class that depends only on the topology, and in particular not on the fluxes. Template:Harvtxt have found a constraint on P using the E₈ gauge theory approach to M-theory pioneered by Diaconescu, Moore, and Witten.

Thus D-branes in IIB are not classified by twisted K-theory after all, but some unknown S-duality-covariant object that inevitably also classifies both fundamental strings and NS5-branes.

However the MMS prescription for calculating twisted K-theory is easily S-covariantized, as the Freed-Witten anomalies respect S-duality. Thus the S-covariantized form of the MMS construction may be applied to construct the S-covariantized twisted K-theory, as a set, without knowing having any geometric description for just what this strange covariant object is. This program has been carried out in a number of papers, such as Template:Harvtxt and Template:Harvtxt, and was also applied to the classification of fluxes by Template:Harvtxt. Template:Harvtxt use this approach to prove Diaconescu, Moore, and Witten's conjectured constraint on the 3-fluxes, and they show that there is an additional term equal to the D3-brane charge. Template:Harvtxt shows that the Klebanov-Strassler cascade of Seiberg dualities consists of a series of S-dual MMS instantons, one for each Seiberg duality. The group, $Z_{N}$ of universality classes of the $S U (M + N) \times S U (M)$ supersymmetric gauge theory is then shown to agree with the S-dual twisted K-theory and not with the original twisted K-theory.

Some authors have proposed radically different solutions to this puzzle. For example, Template:Harvtxt propose that instead of twisted K-theory, II string theory configurations should be classified by elliptic cohomology.

Researchers

Prominent researchers in this area include Ed Witten, Peter Bouwknegt, Angel Uranga, Emanuel Diaconescu, Gregory Moore, Anton Kapustin, Jonathan Rosenberg, Ruben Minasian, Amihay Hanany, Hisham Sati, Nathan Seiberg, Juan Maldacena, Daniel Freed, and Igor Kriz.

Notes

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References

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Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

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15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

References (Condensed Matter Physics)

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

External links

K-theory on arxiv.org

de:K-Theorie fr:K-théorie it:K-teoria ritorta pt:K-Teoria (Física)

↑ Juan Maldacena, Gregory Moore and Nathan Seiberg. D-Brane Instantons and K-Theory Charges. http://arxiv.org/abs/hep-th/0108100

[1] Juan Maldacena, Gregory Moore and Nathan Seiberg. D-Brane Instantons and K-Theory Charges. http://arxiv.org/abs/hep-th/0108100

[1]

Coanalytic set: Difference between revisions

Latest revision as of 15:46, 21 September 2012

Contents

History

Applications

Open problems

K-theory classification of RR fluxes

K-theory classification of D-branes

K-theory charge versus BPS charge

K-theory from tachyon condensation

Twisted K-theory from MMS instantons

Reconciling twisted K-theory and S-duality

Researchers

See also

Notes

References

References (Condensed Matter Physics)

Further reading

External links

Navigation menu

@@ Line 1: / Line 1: @@
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+{{string theory}}
+In [[string theory]], '''the K-theory classification''' refers to a conjectured application of ''[[K-theory]]'' (in [[abstract algebra]] and [[algebraic topology]]) to superstrings, to classify the allowed [[Ramond-Ramond field]] strengths as well as the charges of stable D-[[Membrane (M-theory)|branes]].
+In [[condensed matter physics]] K-theory has also found important applications, specially in the topological classification of [[topological insulator]]s, superconductors and stable Fermi Surfaces ({{harvtxt|Kitaev|2009}}, {{harvtxt|Horava|2005}}).
+== History ==
+This conjecture, applied to D-brane charges, was first proposed by {{harvtxt|Minasian|Moore|1997}}.  It was popularized by {{harvtxt|Witten|1998}} who demonstrated that in [[type IIB]] string theory arises naturally from [[Ashoke Sen]]'s realization of arbitrary D-brane configurations as stacks of [[D9-brane|D9]] and anti-D9-branes after [[tachyon condensation]].
+Such stacks of branes are inconsistent in a non-torsion [[Kalb-Ramond field|Neveu-Schwarz (NS) 3-form]] background, which, as was highlighted by {{harvtxt|Kapustin|2000}}, complicates the extension of the K-theory classification to such cases. {{harvtxt|Bouwknegt|Varghese|2000}} suggested a solution to this problem: D-branes are in general classified by a [[twisted K-theory]], that had earlier been defined by {{harvtxt|Rosenberg|1989}}.
+== Applications ==
+{{string theory}}
+The K-theory classification of D-branes has had numerous applications.  For example, {{harvtxt|Hanany|Kol|2000}} used it to argue that there are eight species of [[orientifold]] one-plane. {{harvtxt|Uranga|2001}} applied the K-theory classification to derive new consistency conditions for [[Compactification (physics)#Flux compactification|flux compactification]]s.  K-theory has also been used to conjecture a formula for the topologies of [[T-duality|T-dual]] manifolds by {{harvtxt|Bouwknegt|Evslin|Varghese|2004}}.  Recently K-theory has been conjectured to classify the [[spinors]] in [[compactification (physics)|compactification]]s on [[generalized complex manifold]]s.
+=== Open problems ===
+Despite these successes, [[Ramond-Ramond field|RR fluxes]] are not quite classified by K-theory.  {{harvtxt|Diaconescu|Moore|Witten|2003}} argued that the K-theory classification is incompatible with [[S-duality]] in [[Type II string theory|IIB string theory]].
+In addition, if one attempts to classify fluxes on a compact ten-dimensional spacetime, then a complication arises due to the self-duality of the RR fluxes.  The duality uses the [[Hodge star]], which depends on the metric and so is continuously valued and in particular is generically irrational.  Thus not all of the RR fluxes, which are interpreted as the [[Chern character]]s in K-theory, can be rational.  However Chern characters are always rational, and so the K-theory classification must be replaced.  One needs to choose a half of the fluxes to quantize, or a ''polarization'' in the [[geometric quantization]]-inspired language of Diaconescu, Moore, and Witten and later of {{harvtxt|Varghese|Sati|2004}}. Alternately one may use the K-theory of a 9-dimensional [[time]] slice as has been done by {{harvtxt|Maldacena|Moore|Seiberg|2001}}.
+==K-theory classification of RR fluxes==
+In the classical limit of [[type II string theory]], which is type II [[supergravity]], the [[Ramond-Ramond field|Ramond-Ramond field strengths]] are [[differential forms]].  In the quantum theory the well-definedness of the partition functions of D-branes implies that the RR field strengths obey [[magnetic monopole#Dirac's quantization|Dirac quantization conditions]] when [[spacetime]] is [[compact space|compact]], or when a spatial slice is compact and one considers only the (magnetic) components of the field strength which lie along the spatial directions.  This led twentieth century physicists to classify RR field strengths using [[cohomology]] with integral coefficients.
+However some authors have argued that the cohomology of spacetime with integral coefficients is too big.  For example, in the presence of Neveu-Schwarz H-flux or non-spin cycles some RR fluxes dictate the presence of D-branes.  In the former case this is a consequence of the supergravity equation of motion which states that the product of a RR flux with the NS 3-form is a D-brane charge density.  Thus the set of topologically distinct RR field strengths that can exist in brane-free configurations is only a subset of the cohomology with integral coefficients.
+This subset is still too big, because some of these classes are related by large gauge transformations.  In QED there are large gauge transformations which add integral multiples of two pi to Wilson loops.  The p-form potentials in type II supergravity theories also enjoy these large gauge transformations, but due to the presence of [[Chern-Simons]] terms in the supergravity actions these large gauge transformations transform not only the p-form potentials but also simultaneously the (p+3)-form field strengths.  Thus to obtain the space of inequivalent field strengths from the forementioned subset of integral cohomology we must quotient by these large gauge transformations.
+The [[Twisted K-theory#How to calculate it|Atiyah-Hirzebruch spectral sequence]] constructs twisted K-theory, with a twist given by the NS 3-form field strength, as a quotient of a subset of the [[cohomology]] with integral coefficients.  In the classical limit, which corresponds to working with rational coefficients, this is precisely the quotient of a subset described above in supergravity.  The quantum corrections come from torsion classes and contain mod 2 torsion corrections due to the Freed-Witten anomaly.
+Thus twisted K-theory classifies the subset of RR field strengths that can exist in the absence of D-branes quotiented by large gauge transformations. Daniel Freed has attempted to extend this classification to include also the RR potentials using differential K-theory.
+==K-theory classification of D-branes==
+K-theory classifies D-branes in noncompact spacetimes, intuitively in spacetimes in which we are not concerned about the flux sourced by the brane having nowhere to go.  While the K-theory of a 10d spacetime classifies D-branes as subsets of that spacetime, if the spacetime is the product of time and a fixed 9-manifold then K-theory also classifies the conserved D-brane charges on each 9-dimensional spatial slice.  While we were required to forget about RR potentials to obtain the K-theory classification of RR field strengths, we are required to forget about RR field strengths to obtain the K-theory classification of D-branes.
+=== K-theory charge versus BPS charge ===
+As has been stressed by [[Petr Hořava (theorist)|Petr Hořava]], the K-theory classification of D-branes is independent of, and in some ways stronger than, the classification of [[Bogomol'nyi Prasad Sommerfield bound|BPS states]].  K-theory appears to classify stable D-branes missed by [[supersymmetry]] based classifications.
+For example, D-branes with torsion charges, that is with charges in the order N cyclic group <math>\mathbf Z_N</math>, attract each other and so can never be BPS.  In fact, N such branes can decay, whereas no superposition of branes that satisfy a Bogomolny bound may ever decay.  However the charge of such branes is conserved modulo N, and this is captured by the K-theory classification but not by a BPS classification.  Such torsion branes have been applied, for example, to model [[Douglas-Shenker strings]] in supersymmetric U(N) [[gauge theory|gauge theories]].
+===K-theory from tachyon condensation===
+[[Ashoke Sen]] has conjectured that, in the absence of a topologically nontrivial NS 3-form flux, all IIB brane configurations can be obtained from stacks of spacefilling D9 and anti D9 branes via [[tachyon condensation]].  The topology of the resulting branes is encoded in the topology of the gauge bundle on the stack of the spacefilling branes.  The topology of the gauge bundle of a stack of D9s and anti D9s can be decomposed into a gauge bundle on the D9's and another bundle on the anti D9's.  Tachyon condensation transforms such a pair of bundles to another pair in which the same bundle is direct summed with each component in the pair.  Thus the tachyon condensation invariant quantity, that is, the charge which is conserved by the tachyon condensation process, is not a pair of bundles but rather the equivalence class of a pair of bundles under direct sums of the same bundle on both sides of the pair.  This is precisely the usual construction of [[topological K-theory]].  Thus the gauge bundles on stacks of D9's and anti-D9's are classified by topological K-theory.  If Sen's conjecture is right, all D-brane configurations in type IIB are then classified by K-theory.  [[Petr Hořava (theorist)|Petr Horava]] has extended this conjecture to type IIA using D8-branes.
+===Twisted K-theory from MMS instantons===
+While the tachyon condensation picture of the K-theory classification classifies D-branes as subsets of a 10-dimensional spacetime with no NS 3-form flux, the Maldacena, Moore, Seiberg picture classifies stable D-branes with finite mass as subsets of a 9-dimensional spatial slice of spacetime.
+The central observation is that D-branes are not classified by integral homology because Dp-branes wrapping certain cycles suffer from a Freed-Witten anomaly, which is cancelled by the insertion of D(p-2)-branes and sometimes D(p-4)-branes that end on the afflicted Dp-brane.  These inserted branes may either continue to infinity, in which case the composite object has an infinite mass, or else they may end on an anti-Dp-brane, in which case the total Dp-brane charge is zero.  In either case, one may wish to remove the anomalous Dp-branes from the spectrum, leaving only a subset of the original integral cohomology.
+The inserted branes are unstable.  To see this, imagine that they extend in time away (into the past) from the anomalous brane.  This corresponds to a process in which the inserted branes decay via a Dp-brane that forms, wraps the forementioned cycle and then disappears.  MMS<ref>[[Juan Maldacena]], [[Greg Moore (physicist)|Gregory Moore]] and [[Nathan Seiberg]]. ''D-Brane Instantons and K-Theory Charges''. http://arxiv.org/abs/hep-th/0108100</ref> refer to this process as an instanton, although really it need not be instantonic.
+The conserved charges are thus the nonanomolous subset quotiented by the unstable insertions.  This is precisely the [[Twisted K-theory#How to calculate it|Atiyah-Hirzebruch spectral sequence]] construction of twisted K-theory as a set.
+==Reconciling twisted K-theory and S-duality==
+Diaconescu, Moore, and Witten have pointed out that the twisted K-theory classification is not compatible with the [[S-duality]] covariance of type IIB string theory.  For example, consider the constraint on the [[Ramond-Ramond field|Ramond-Ramond 3-form field strength]] G<sub>3</sub> in the [[Twisted K-theory#How to calculate it|Atiyah-Hirzebruch spectral sequence]] (AHSS):
+:<math>  d_3G_3=Sq^3G_3+H\cup G_3=G_3\cup G_3+H\cup G_3=0
+</math>
+where d<sub>3</sub>=Sq<sup>3</sup>+H is the first nontrivial differential in the AHSS, Sq<sup>3</sup> is the third [[Steenrod square]] and the last equality follows from the fact that the nth Steenrod square acting on any n-form x is x<math>\cup</math>x.
+The above equation is not invariant under S-duality, which exchanges G<sub>3</sub> and H.  Instead Diaconescu, Moore, and Witten have proposed the following S-duality covariant extension
+:<math>  G_3\cup G_3+H\cup G_3+H\cup H=P
+</math>
+where P is an unknown characteristic class that depends only on the topology, and in particular not on the fluxes. {{harvtxt|Diaconescu|Freed|Moore|2007}} have found a constraint on P using the [[ME8|E<sub>8</sub> gauge theory approach to M-theory]] pioneered by Diaconescu, Moore, and Witten.
+Thus D-branes in IIB are not classified by twisted K-theory after all, but some unknown S-duality-covariant object that inevitably also classifies both fundamental strings and [[NS5-brane]]s.
+However the MMS prescription for calculating twisted K-theory is easily S-covariantized, as the Freed-Witten anomalies respect S-duality.  Thus the S-covariantized form of the MMS construction may be applied to construct the S-covariantized twisted K-theory, as a set, without knowing having any geometric description for just what this strange covariant object is.  This program has been carried out in a number of papers, such as {{harvtxt|Evslin|Varadarajan|2003}} and {{harvtxt|Evslin|2003a}}, and was also applied to the classification of fluxes by {{harvtxt|Evslin|2003b}}.  {{harvtxt|Bouwknegt|Evslin|Jurco|Varghese|2006}} use this approach to prove Diaconescu, Moore, and Witten's conjectured constraint on the 3-fluxes, and they show that there is an additional term equal to the D3-brane charge. {{harvtxt|Evslin|2006}} shows that the [[Klebanov-Strassler cascade]] of [[Seiberg duality|Seiberg dualities]] consists of a series of S-dual MMS instantons, one for each Seiberg duality.  The group, <math>\mathbf Z_N</math> of universality classes of the <math>SU(M+N)\times SU(M)</math> supersymmetric [[gauge theory]] is then shown to agree with the S-dual twisted K-theory and not with the original twisted K-theory.
+Some authors have proposed radically different solutions to this puzzle.  For example, {{harvtxt|Kriz|Sati|2005}} propose that instead of twisted K-theory, II string theory configurations should be classified by [[elliptic cohomology]].
+==Researchers==
+Prominent researchers in this area include [[Ed Witten]], Peter Bouwknegt, Angel Uranga, Emanuel Diaconescu, [[Greg Moore (physicist)|Gregory Moore]], [[Anton Kapustin]], [[Jonathan Rosenberg (mathematician)|Jonathan Rosenberg]], Ruben Minasian, Amihay Hanany, Hisham Sati, [[Nathan Seiberg]], [[Juan Maldacena]], [[Daniel Freed]], and Igor Kriz.
+==See also==
+*[[Twisted K-theory]]
+*[[Ramond-Ramond field]]
+*[[Kalb-Ramond field]]
+*[[D-brane]]
+==Notes==
+{{reflist}}
+==References==
+*{{citation
+ | last1 = Bouwknegt | first1 = Peter
+ | last2 = Evslin | first2 = Jarah
+ | last3 = Jurco | first3 = Branislav
+ | last4 = Varghese | first4 = Mathai | authorlink3 = Mathai Varghese
+ | last5 = Sati | first5 = Hisham
+ | title = Flux Compactifications on Projective Spaces and The S-Duality Puzzle
+ | journal = [[Advances in Theoretical and Mathematical Physics]]
+ | volume = 10 | year = 2006 | pages = 345–394
+ | arxiv = hep-th/0501110|bibcode = 2005hep.th....1110B }}.
+*{{citation
+ | last1 = Bouwknegt | first1 = Peter
+ | last2 = Evslin | first2 = Jarah
+ | last3 = Varghese | first3 = Mathai | authorlink3 = Mathai Varghese
+ | title = T-Duality: Topology Change from H-flux
+ | journal = [[Communications in Mathematical Physics]]
+ | volume = 249 | year = 2004 | pages = 383–415
+ | doi = 10.1007/s00220-004-1115-6
+ | arxiv = hep-th/0306062| issue = 2|bibcode = 2004CMaPh.249..383B }}.
+*{{citation
+ | last1 = Bouwknegt | first1 = Peter
+ | last2 = Varghese | first2 = Mathai | authorlink2 = Mathai Varghese
+ | title = D-branes, B-fields and twisted K-theory
+ | journal = [[Journal of High Energy Physics]]
+ | year = 2000
+ | volume = 0003
+ | issue = 007
+ | doi = 10.1088/1126-6708/2000/03/007
+ | pages = 007
+ | arxiv = hep-th/0002023|bibcode = 2000JHEP...03..007B }}.
+*{{citation
+ | last1 = Diaconescu | first1 = Emanuel
+ | last2 = Freed | first2 = Daniel S. | authorlink2=Dan Freed
+ | last3 = Moore | first3 = Gregory
+ | contribution = The M-theory 3-form and E<sub>8</sub> gauge theory
+ | title = Elliptic Cohomology: Geometry, Applications, and Higher Chromatic Analogues
+ | editor1-last = Miller | editor1-first = Haynes R.
+ | editor2-last = Ravenel | editor2-first = Douglas C.
+ | publisher = Cambridge University Press
+ | year = 2007 | pages = 44–88
+ | arxiv = hep-th/0312069|bibcode = 2003hep.th...12069D }}.
+*{{citation
+ | last1 = Diaconescu | first1 = Emanuel
+ | last2 = Moore | first2 = Gregory
+ | last3 = Witten | first3 = Edward | authorlink3 = Edward Witten
+ | title = E<sub>8</sub> Gauge Theory, and a Derivation of K-Theory from M-Theory
+ | journal = [[Advances in Theoretical and Mathematical Physics]]
+ | volume = 6 | year = 2003 | pages = 1031–1134
+ | arxiv = hep-th/0005090|bibcode = 2000hep.th....5090D }}.
+*{{citation
+ | last = Evslin | first = Jarah
+ | title = IIB Soliton Spectra with All Fluxes Activated
+ | journal = [[Nuclear Physics B]]
+ | volume = 657
+ | year = 2003a
+ | pages = 139–168
+ | doi = 10.1016/S0550-3213(03)00154-8|arxiv = hep-th/0211172 |bibcode = 2003NuPhB.657..139E }}.
+*{{citation
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+ | title = Twisted K-Theory from Monodromies
+ | journal = [[Journal of High Energy Physics]]
+ | volume = 0305 | year = 2003b | issue = 030
+ | doi = 10.1088/1126-6708/2003/05/030
+ | pages = 030
+ | arxiv = hep-th/0302081|bibcode = 2003JHEP...05..030E }}.
+*{{citation
+ | last = Evslin | first = Jarah
+ | contribution = The Cascade is a MMS Instanton
+ | title = Advances in Soliton Research
+ | publisher = Nova Science Publishers
+ | year = 2006
+ | pages = 153–187
+ | arxiv = hep-th/0405210|bibcode = 2004hep.th....5210E }}.
+*{{citation
+ | last1 = Evslin | first1 = Jarah
+ | last2 = Varadarajan | first2 = Uday
+ | title = K-Theory and S-Duality: Starting Over from Square 3
+ | journal = Journal of High Energy Physics
+ | volume = 0303 | year = 2003 | issue = 026
+ | doi = 10.1088/1126-6708/2003/03/026
+ | pages = 026
+ | arxiv = hep-th/0112084|bibcode = 2003JHEP...03..026E }}.
+*{{citation
+ | last = Hanany | first1 = Amihay
+ | last2 = Kol | first2 = Barak | authorlink2 = Barak Kol
+ | title = On Orientifolds, Discrete Torsion, Branes and M Theory
+ | journal = Journal of High Energy Physics
+ | year = 2000
+ | volume = 0006
+ | issue = 013
+ | doi = 10.1088/1126-6708/2000/06/013
+ | pages = 013
+ | arxiv = hep-th/0003025|bibcode = 2000JHEP...06..013H }}.
+*{{citation
+ | last = Kapustin
+ | first = Anton
+ | title = D-branes in a topologically nontrivial B-field
+ | journal = [[Advances in Theoretical and Mathematical Physics]]
+ | volume = 4
+ | year = 2000
+ | pages = 127–154
+ | arxiv = hep-th/9909089|bibcode = 1999hep.th....9089K }}.
+*{{citation
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+ | last2 = Sati | first2 = Hisham
+ | title = Type IIB String Theory, S-Duality, and Generalized Cohomology
+ | journal = Nuclear Physics B
+ | volume = 715 | year = 2005 | pages = 639–664
+ | doi = 10.1016/j.nuclphysb.2005.02.016
+ | arxiv = hep-th/0410293| issue = 3|bibcode = 2005NuPhB.715..639K }}.
+*{{citation
+ | last1 = Maldacena | first1 = Juan | authorlink1 = Juan Maldacena
+ | last2 = Moore | first2 = Gregory
+ | last3 = Seiberg | first3 = Nathan | authorlink3 = Nathan Seiberg
+ | title = D-Brane Instantons and K-Theory Charges
+ | journal = Journal of High Energy Physics
+ | volume = 0111 | year = 2001 | issue = 062
+ | doi = 10.1088/1126-6708/2001/11/062
+ | pages = 062
+ | arxiv = hep-th/0108100|bibcode = 2001JHEP...11..062M }}.
+*{{citation
+ | last1 = Minasian | first1 = Ruben
+ | last2 = Moore | first2 = Gregory
+ | title = K-theory and Ramond-Ramond charge
+ | journal = Journal of High Energy Physics
+ | volume = 9711
+ | year = 1997
+ | issue = 002
+ | doi =10.1088/1126-6708/1997/11/002
+ | pages = 002
+ | arxiv = hep-th/9710230|bibcode = 1997JHEP...11..002M }}.
+*{{citation
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+ | last2 = Szabo | first2 = Richard J. | authorlink2 = Richard J. Szabo
+ | title = Constructing D-Branes from K-Theory
+ | journal = Advances in Theoretical and Mathematical Physics
+ | volume = 3 | year = 1999 | pages = 889–1025
+ | arxiv = hep-th/9907140|bibcode = 1999hep.th....7140O }}.
+*{{citation
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+ | title = Continuous-Trace Algebras from the Bundle Theoretic Point of View
+ | journal = Journal of the Australian Mathematical Society, Series A
+ | volume = 47 | year = 1989 | pages = 368–381
+ | url = http://anziamj.austms.org.au/JAMSA/V47/Part3/Rosenberg.html
+ | doi = 10.1017/S1446788700033097
+ | issue = 03}}.
+*{{citation
+ | last = Uranga | first = Angel M.
+ | title = D-brane probes, RR tadpole cancellation and K-theory charge
+ | journal = Nuclear Physics B
+ | volume = 598 | year = 2001 | pages = 225–246
+ | doi = 10.1016/S0550-3213(00)00787-2
+ | arxiv = hep-th/0011048|bibcode = 2001NuPhB.598..225U }}.
+*{{citation
+ | last1 = Varghese | first1 = Mathai | authorlink1 = Mathai Varghese
+ | last2 = Sati | first2 = Hisham
+ | title = Some Relations between Twisted K-theory and E<sub>8</sub> Gauge Theory
+ | journal = Journal of High Energy Physics
+ | volume = 0403 | year = 2004 | issue = 016
+ | doi = 10.1088/1126-6708/2004/03/016
+ | pages = 016
+ | arxiv = hep-th/0312033|bibcode = 2004JHEP...03..016M }}.
+*{{citation
+ | last = Witten | first = Edward | authorlink = Edward Witten
+ | title = D-Branes and K-Theory
+ | journal = Journal of High Energy Physics
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+ | doi = 10.1088/1126-6708/1998/12/019
+ | pages = 019
+ | arxiv = hep-th/9810188|bibcode = 1998JHEP...12..019W }}.
+==References (Condensed Matter Physics)==
+*{{citation
+ | last = Kitaev | first = Alexei | authorlink = Alexei Kitaev
+ | title = Periodic table for topological insulators and superconductors
+ | journal = Arxiv (cond-mat)
+ | year = 2009
+ | arxiv = 0901.2686|bibcode = 2009AIPC.1134...22K |doi = 10.1063/1.3149495 }}.
+*{{citation
+ | last = Horava | first = Petr
+ | title = Stability of Fermi Surfaces and K Theory
+ | journal = Physical Review Letters
+ | volume = 95
+ | year = 2005
+ | issue = 016405}}.
+==Further reading==
+An excellent introduction to the [[K-theory]] classification of [[D-branes]] in 10 dimensions via [[Ashoke Sen]]'s conjecture is the original paper "D-branes and K-theory" by [[Edward Witten]]; there is also an extensive review by {{harvtxt|Olsen|Szabo|1999}}.
+A very comprehensible introduction to the [[twisted K-theory]] classification of conserved D-brane charges on a 9-dimensional [[timeslice]] in the presence of [[Neveu-Schwarz flux]] is {{harvtxt|Maldacena|Moore|Seiberg|2001}}.
+==External links==
+*[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=296918 K-theory on arxiv.org]
+[[Category:String theory]]
+[[Category:Algebra]]
+[[Category:K-theory]]
+[[de:K-Theorie]]
+[[fr:K-théorie]]
+[[it:K-teoria ritorta]]
+[[pt:K-Teoria (Física)]]

Coanalytic set: Difference between revisions

Latest revision as of 15:46, 21 September 2012

History

Applications

Open problems

K-theory classification of RR fluxes

K-theory classification of D-branes

K-theory charge versus BPS charge

K-theory from tachyon condensation

Twisted K-theory from MMS instantons

Reconciling twisted K-theory and S-duality

Researchers

See also

Notes

References

References (Condensed Matter Physics)

Further reading

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