Equivariant K-theory and Equivariant Cohomology

TL;DR

This paper establishes a relationship between T-equivariant K-theory and equivariant cohomology for abelian compact Lie groups, extending key results from cohomology to K-theory with complex coefficients.

Contribution

It provides a new description of equivariant K-theory in terms of equivariant cohomology and extends important results from cohomology to K-theory.

Findings

Describes T-equivariant K-theory via equivariant cohomology

Extends Chang-Skjelbred and Goresky-Kottwitz-MacPherson results to K-theory

Provides applications in the appendix

Abstract

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and Goresky-Kottwitz-MacPherson from equivariant cohomology to equivariant K-theory.