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- Equivariant_cohomology abstract "In mathematics, equivariant 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 X with action of a topological group G 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: If X is a manifold, G a compact Lie group and is the field of real numbers or the field of complex numbers (the most typical situation), then the above cohomology may be computed using so-called Cartan model (see equivariant differential forms.)The construction should not be confused as a more naive cohomology of invariant differential forms: if G is a compact Lie group, then, by the averaging argument, any form may be made invariant; thus, cohomology of invariant differential forms does not yield new information.The koszul duality is known to hold between equivariant cohomology and ordinary cohomology.".
- Equivariant_cohomology wikiPageExternalLink notesmontreal.pdf.
- Equivariant_cohomology wikiPageExternalLink rtx110300423p.pdf.
- Equivariant_cohomology wikiPageExternalLink clermontu.pdf.
- Equivariant_cohomology wikiPageExternalLink mylecture-equivcoh.pdf.
- Equivariant_cohomology wikiPageID "2976342".
- Equivariant_cohomology wikiPageRevisionID "605054401".
- Equivariant_cohomology hasPhotoCollection Equivariant_cohomology.
- Equivariant_cohomology id "e/e036090".
- Equivariant_cohomology title "Equivariant cohomology".
- Equivariant_cohomology subject Category:Algebraic_topology.
- Equivariant_cohomology subject Category:Group_actions.
- Equivariant_cohomology subject Category:Homotopy_theory.
- Equivariant_cohomology subject Category:Symplectic_topology.
- Equivariant_cohomology type Abstraction100002137.
- Equivariant_cohomology type Act100030358.
- Equivariant_cohomology type Event100029378.
- Equivariant_cohomology type GroupAction101080366.
- Equivariant_cohomology type GroupActions.
- Equivariant_cohomology type PsychologicalFeature100023100.
- Equivariant_cohomology type YagoPermanentlyLocatedEntity.
- Equivariant_cohomology comment "In mathematics, equivariant 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.".
- Equivariant_cohomology label "Equivariant cohomology".
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- Equivariant_cohomology sameAs Q5384738.
- Equivariant_cohomology sameAs Q5384738.
- Equivariant_cohomology sameAs Equivariant_cohomology.
- Equivariant_cohomology wasDerivedFrom Equivariant_cohomology?oldid=605054401.
- Equivariant_cohomology isPrimaryTopicOf Equivariant_cohomology.