Equivariant Cohomology

In mathematics, equivariant cohomology is a theory from algebraic topology which applies to spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory.

Specifically, given a group (discrete or not), a topological space and an action

equivariant cohomology determines a graded ring

the equivariant cohomology ring. If is the trivial group, this is just the ordinary cohomology ring of, whereas if is contractible, it reduces to the group cohomology of .