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In mathematics, a '''Brieskorn manifold''' or '''Brieskorn–Pham manifold''',  introduced by {{harvs|txt|last=Brieskorn|year=1966|year2=1966b}}, is the intersection of a small sphere around the origin with the singular hypersurface
:<math>x_1^{k_1}+\cdots+x_n^{k_n}=0</math>
studied by {{harvtxt|Pham|1965}}.


Brieskorn manifolds give examples of [[exotic sphere]]s.


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==References==


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*{{citation |mr=0198497 |last=Brieskorn |first= Egbert V. |title=Examples of singular normal complex spaces which are topological manifolds |journal=[[Proceedings of the National Academy of Sciences]] |volume= 55|year= 1966|pages= 1395–1397 |issue=6 |doi=10.1073/pnas.55.6.1395 |pmc=224331}}
*{{citation |mr=0206972 |last=Brieskorn |first= Egbert |title=Beispiele zur Differentialtopologie von Singularitäten |journal=Invent. Math. |volume=2 |year=1966b |issue=1 |pages=1–14 |doi=10.1007/BF01403388}}
*{{citation |first=Friedrich |last=Hirzebruch |first2= Karl Heinz |last2=Mayer |title=O(n)-Mannigfaligkeiten, Exotische Sphären und Singularitäten |series= Lecture Notes in Mathematics |volume= 57 |publisher= [[Springer-Verlag]] |publication-place= Berlin-New York |year= 1968 |mr= 0229251 |doi=10.1007/BFb0074355}} This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds.
*{{Citation | last1=Pham | first1=Frédéric | title=Formules de Picard-Lefschetz généralisées et ramification des intégrales | mr=0195868  | year=1965 | journal=Bulletin de la Société Mathématique de France | issn=0037-9484 | volume=93 | pages=333–367}}
 
[[Category:Singularity theory]]

Revision as of 19:29, 11 August 2013

In mathematics, a Brieskorn manifold or Brieskorn–Pham manifold, introduced by Template:Harvs, is the intersection of a small sphere around the origin with the singular hypersurface

x1k1++xnkn=0

studied by Template:Harvtxt.

Brieskorn manifolds give examples of exotic spheres.

References

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    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.

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