Equivariant Cohomology

The equivariant cohomology along with the celebrated localization formula provides a strong tool in computing usual cohomology of a geometric object equipped with action of a group. It encompasses several localization theorems in geometry and complex analysis (which have roots in the residue theorem in complex analysis). Surprisingly, in a rich class of examples, known as GKM spaces (named after Goresky, Kottwitz and McPherson), this approach enables one to reduce the description of cohomology, and doing computations in the cohomology, to combinatorics of the so-called GKM graphs. Toric varieties, Grassmannians, flag varieties and many other important examples of varieties are special cases of GKM spaces.

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