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About: Equivariant cohomology

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In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. Specifically, the equivariant cohomology ring of a space with action of a topological group is defined as the ordinary cohomology ring with coefficient ring of the homotopy quotient :

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  • In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. Specifically, the equivariant cohomology ring of a space with action of a topological group is defined as the ordinary cohomology ring with coefficient ring of the homotopy quotient : If is the trivial group, this is the ordinary cohomology ring of , whereas if is contractible, it reduces to the cohomology ring of the classifying space (that is, the group cohomology of when G is finite.) If G acts freely on X, then the canonical map is a homotopy equivalence and so one gets: (en)
  • 대수적 위상수학에서 등변 코호몰로지(等變cohomology, 영어: equivariant cohomology)는 군 코호몰로지와 특이 코호몰로지를 일반화하는 코호몰로지 이론이다. (ko)
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  • e/e036090 (en)
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  • Equivariant cohomology (en)
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  • 대수적 위상수학에서 등변 코호몰로지(等變cohomology, 영어: equivariant cohomology)는 군 코호몰로지와 특이 코호몰로지를 일반화하는 코호몰로지 이론이다. (ko)
  • In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. Specifically, the equivariant cohomology ring of a space with action of a topological group is defined as the ordinary cohomology ring with coefficient ring of the homotopy quotient : (en)
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  • Equivariant cohomology (en)
  • 등변 코호몰로지 (ko)
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