About: Rokhlin's theorem

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In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group , is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952.

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rdfs:label	ロホリンの定理 (ja) Rokhlin's theorem (en) Теорема Рохлина о сигнатуре (ru)
rdfs:comment	In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group , is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952. (en) 数学の一分野である 4次元の位相幾何学（トポロジー)において、ロホリンの定理とは滑らかでコンパクトな 4次元多様体 M がスピン構造を持つならば(同値だが、第2スティーフェル・ホイットニー類 w2(M) = 0 であれば)、多様体の交叉形式の(signature)、第2コホモロジー群の二次形式 H2(M)は、16 で割り切れるという定理である。この定理は、1952年に(Vladimir Rokhlin)が証明した。 (ja) Теорема Рохлина о сигнатуре — теорема четырёхмерной топологии.Доказана Владимиром Абрамовичем Рохлиным в 1952 году. (ru)
dcterms:subject	4-manifolds Surgery theory Theorems in topology Differential structures Geometric topology
Wikipage page ID	7031816 (xsd:integer)
Wikipage revision ID	1106025242 (xsd:integer)
Link from a Wikipage to another Wikipage	Cahit Arf Cambridge University Press Princeton University Press Robion Kirby Enriques surface Arf invariant E8 manifold Stiefel–Whitney class 4-manifolds Surgery theory Theorems in topology Genus of a multiplicative sequence Smooth structure Friedrich Hirzebruch Differential structures Â genus Mazur manifold Poincaré duality American Mathematical Society Hirzebruch signature theorem Simply connected space Quadratic form Geometric topology Atiyah–Singer index theorem Intersection form (4-manifold) Isadore Singer Armand Borel John Milnor K3 surface Torsion (algebra) Differentiable manifold Manifold Michael Atiyah Michael Freedman Michel Kervaire Casson invariant Topological manifold Signature (topology) Unimodular lattice Spin structure Kirby–Siebenmann invariant Poincaré homology sphere Vladimir Rokhlin (Soviet mathematician) Cohomology group Stable homotopy group of spheres Spin manifold
Link from a Wikipage to an external page	https://www.semanticscholar.org/paper/An-elementary-proof-of-Rochlin''s-signature-theorem-Matsumoto/ace0e29960824a5d10923f06f04f46ec285f03a1 https://www.maths.ed.ac.uk/~v1ranick/papers/matumoto5.pdf
sameAs	Rokhlin's theorem Rokhlin's theorem Rokhlin's theorem Rokhlin's theorem Rokhlin's theorem Rokhlin's theorem
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authorlink	Robion Kirby (en)
first	Robion (en)
last	Kirby (en)
year	1989 (xsd:integer)
has abstract	In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group , is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952. (en) 数学の一分野である 4次元の位相幾何学（トポロジー)において、ロホリンの定理とは滑らかでコンパクトな 4次元多様体 M がスピン構造を持つならば(同値だが、第2スティーフェル・ホイットニー類 w2(M) = 0 であれば)、多様体の交叉形式の(signature)、第2コホモロジー群の二次形式 H2(M)は、16 で割り切れるという定理である。この定理は、1952年に(Vladimir Rokhlin)が証明した。 (ja) Теорема Рохлина о сигнатуре — теорема четырёхмерной топологии.Доказана Владимиром Абрамовичем Рохлиным в 1952 году. (ru)
prov:wasDerivedFrom	wikipedia-en:Rokhlin's_theorem?oldid=1106025242&ns=0
page length (characters) of wiki page	10094 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Rokhlin's_theorem
is Link from a Wikipage to another Wikipage of	Homotopy groups of spheres Vladimir Abramovich Rokhlin Donaldson's theorem E8 manifold Intersection form of a 4-manifold Smooth structure Atiyah–Singer index theorem

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