Current algebra - Revision history

en>BD2412: Fixing links to disambiguation pages using AWB

2014-05-11T18:05:39Z

Fixing links to disambiguation pages using AWB

← Older revision		Revision as of 20:05, 11 May 2014
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	~~Nice car car warranty warranty~~ to ~~satisfy~~ you, ~~my title is extended car warranty Araceli~~ [http://~~Www~~.~~Mpp~~.~~com/warranty-plans/used-car-warranties~~.~~htm Oquendo] [http://extended-car-warranty-Services-Review~~.~~toptenreviews~~.~~com/ auto warranty] but I~~ don't ~~like when individuals use my complete name~~. ~~The thing she adores most is flower arranging and she is attempting~~ to ~~make~~ it ~~a profession~~. ~~After being out~~ of ~~my occupation~~ for ~~many years I grew~~ to ~~become a~~ [http://www.Ag.~~state.mn.us~~/~~consumer~~/~~cars/mncarlaws/mncarlaws_2~~.~~asp manufacturing]~~ and ~~distribution officer but I strategy~~ on ~~altering it~~. ~~Her family lives~~ in ~~Delaware but she needs~~ to ~~move because of her family~~.<br><br>~~Look at my blog - [http://Www~~.~~you3dview~~.~~com/users/FJasso Www.you3dview~~.~~com]~~

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en>Wavelength: inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

2014-02-20T03:39:38Z

inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

← Older revision		Revision as of 05:39, 20 February 2014
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	In [~~[differential topology]], the '''Whitney immersion theorem''' states that for <math>m>1<~~/~~math>, any smooth <math>m<~~/~~math>~~-~~dimensional [[manifold]] (required also to be [[Hausdorff space\|Hausdorff]] and [[second~~-~~countable]]) has a one~~-~~to-one [[immersion (mathematics)\|immersion~~]~~] in~~ [~~[Euclidean space\|Euclidean]] <math>2m<~~/~~math>~~-~~space, and a (not necessarily one~~-to-~~one) immersion in <math>(2m~~-~~1)</math>-space~~. ~~Similarly, every smooth <math>m<~~/~~math>-dimensional manifold can be immersed in the <math>2m-1</math>-dimensional sphere (this removes the <math>m>1</math> constraint)~~.		Nice car car warranty warranty to satisfy you, my title is extended car warranty Araceli [http://Www.Mpp.com/warranty-plans/used-car-warranties.htm Oquendo] [http://extended-car-warranty-Services-Review.toptenreviews.com/ auto warranty] but I don't like when individuals use my complete name. The thing she adores most is flower arranging and she is attempting to make it a profession. After being out of my occupation for many years I grew to become a [http://www.Ag.state.mn.us/consumer/cars/mncarlaws/mncarlaws_2.asp manufacturing] and distribution officer but I strategy on altering it. Her family lives in Delaware but she needs to move because of her family.<br><br>Look at my blog - [http://Www.you3dview.com/users/FJasso Www.you3dview.com]

	The ~~weak version,~~ for ~~<math>2m+1</math>, is due~~ to [~~[Transversality (mathematics)\|transversality]] ([[general position]], [[dimension counting]])~~: ~~two ''m''-dimensional manifolds in <math>\mathbf{R}^{2m}<~~/~~math> intersect generically in a 0-dimensional space~~.

	~~==Further Results==~~
	~~Massey went on to prove that every n-dimensional manifold is cobordant to a manifold that immerses in <math>S^{2n-a(n)}<~~/~~math> where <math>a(n)<~~/~~math> is the number of 1's that appear in the binary expansion of <math>n<~~/~~math>~~. ~~In the same paper, Massey proved that for every n there is manifold (which happens~~ to ~~be a product~~ of ~~real projective spaces) that does not immerse in~~ <~~math~~>~~S^{2n-1-a(n)}</math>. The conjecture that every n-manifold immerses in~~ <~~math~~>~~S^{2n~~-~~a(n)}</math> became known as the '''Immersion Conjecture''' which was eventually solved in the affirmative by Ralph Cohen {{Harv\|Cohen\|1985}}.~~

	~~==See also==~~
	*[[Whitney embedding theorem]]

	~~== References ==~~
	* {{citation
	~~\|doi=10.2307/1971304~~
	~~\|first=Ralph L.~~
	~~\|last=Cohen~~
	~~\|title=The Immersion Conjecture for Differentiable Manifolds~~
	~~\|journal=The Annals of Mathematics~~
	~~\|year=1985~~
	~~\|pages=237–328~~
	~~\|jstor=1971304~~
	~~\|volume=122~~
	~~\|issue=2~~
	~~\|publisher=Annals of Mathematics~~
	}}

	~~== External links ==~~
	* [http://~~maths~~.~~swan~~.~~ac.uk~~/~~staff~~/~~jhg/papers/thesis-final~~.~~pdf Stiefel-Whitney Characteristic Classes and the Immersion Conjecture~~]~~, by Jeffrey Giansiracusa, 2003~~
	*:Exposition of Cohen's work

	~~[[Category:Theorems in differential topology]]~~


	~~{{topology-stub}}~~

en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q1454725

2013-03-13T17:14:45Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q1454725

← Older revision		Revision as of 19:14, 13 March 2013
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	~~Friends contact her Felicidad~~ and ~~her spouse doesn't like it at all~~. ~~What she loves performing~~ is to ~~perform croquet but she hasn~~'~~t made~~ a ~~dime with it~~. ~~Managing individuals~~ is ~~how I make cash and it~~'s ~~some thing I truly appreciate~~. ~~Arizona~~ is ~~her birth location and she will by no means transfer~~.<br><br>~~Visit my website: extended auto warranty,~~ [http://~~www~~.~~Naadagam~~.~~com~~/~~profile~~.~~php?u=JoMarina simply click~~ the ~~up coming web site~~],		In [[differential topology]], the '''Whitney immersion theorem''' states that for <math>m>1</math>, any smooth <math>m</math>-dimensional [[manifold]] (required also to be [[Hausdorff space\|Hausdorff]] and [[second-countable]]) has a one-to-one [[immersion (mathematics)\|immersion]] in [[Euclidean space\|Euclidean]] <math>2m</math>-space, and a (not necessarily one-to-one) immersion in <math>(2m-1)</math>-space. Similarly, every smooth <math>m</math>-dimensional manifold can be immersed in the <math>2m-1</math>-dimensional sphere (this removes the <math>m>1</math> constraint).

			The weak version, for <math>2m+1</math>, is due to [[Transversality (mathematics)\|transversality]] ([[general position]], [[dimension counting]]): two ''m''-dimensional manifolds in <math>\mathbf{R}^{2m}</math> intersect generically in a 0-dimensional space.

			==Further Results==
			Massey went on to prove that every n-dimensional manifold is cobordant to a manifold that immerses in <math>S^{2n-a(n)}</math> where <math>a(n)</math> is the number of 1's that appear in the binary expansion of <math>n</math>. In the same paper, Massey proved that for every n there is manifold (which happens to be a product of real projective spaces) that does not immerse in <math>S^{2n-1-a(n)}</math>. The conjecture that every n-manifold immerses in <math>S^{2n-a(n)}</math> became known as the '''Immersion Conjecture''' which was eventually solved in the affirmative by Ralph Cohen {{Harv\|Cohen\|1985}}.

			==See also==
			*[[Whitney embedding theorem]]

			== References ==
			* {{citation
			\|doi=10.2307/1971304
			\|first=Ralph L.
			\|last=Cohen
			\|title=The Immersion Conjecture for Differentiable Manifolds
			\|journal=The Annals of Mathematics
			\|year=1985
			\|pages=237–328
			\|jstor=1971304
			\|volume=122
			\|issue=2
			\|publisher=Annals of Mathematics
			}}

			== External links ==
			* [http://maths.swan.ac.uk/staff/jhg/papers/thesis-final.pdf Stiefel-Whitney Characteristic Classes and the Immersion Conjecture], by Jeffrey Giansiracusa, 2003
			*:Exposition of Cohen's work

			[[Category:Theorems in differential topology]]


			{{topology-stub}}

en>ChuispastonBot: r2.7.1) (Robot: Adding de:Stromalgebra

2012-02-10T16:57:16Z

r2.7.1) (Robot: Adding de:Stromalgebra

New page

Friends contact her Felicidad and her spouse doesn't like it at all. What she loves performing is to perform croquet but she hasn't made a dime with it. Managing individuals is how I make cash and it's some thing I truly appreciate. Arizona is her birth location and she will by no means transfer.<br><br>Visit my website: extended auto warranty, [http://www.Naadagam.com/profile.php?u=JoMarina simply click the up coming web site],