2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74541This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the combinatorial data of a skeleton of G-orbits on X. We give both a geometric definition and the traditional definition of equivariant cohomology. We include a discussion of the moment map and an algorithm for finding a set of generators for the equivariant cohomology of X. Many examples and explicit calculations are provided.20 pages; an expository paper delivered at the 2004 AMS conference for young algebraic geometersAlgebraic GeometryAlgebraic Topology55N51; 14F43text