Equivariant cohomology
= Equivariant cohomology
{title2=$H_G^*(X;R)=H^*(EG\times_GX;R)$}
{wiki}
The Borel version of equivariant cohomology is the ordinary <cohomology> of the <Borel construction>. It retains information about both the space and its <group action>. For a point it is the cohomology of the <classifying space>; for a free action with the usual bundle hypotheses it is the cohomology of the orbit space.