The equivariant cohomology of a 
-space 
is the ordinary cohomology
of the homotopy quotient space 
. It combines the topology of 
with the action of 
. For a point it gives the cohomology of the classifying space
,
while a free action gives the cohomology of the orbit space.
Equivariant Cohomology
See also
Cohomology, Group Action, Quotient SpaceExplore with Wolfram|Alpha
References
Guillemin, V. and Sternberg, S. Supersymmetry and Equivariant de Rham Theory. Berlin, Germany: Springer-Verlag, 1999.Cite this as:
Weisstein, Eric W. "Equivariant Cohomology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EquivariantCohomology.html