English

A stroll in equivariant $K$-theory

K-Theory and Homology 2023-09-19 v2 Algebraic Topology

Abstract

Equivariant KK-theory is a generalized equivariant cohomology theory which is a hybrid of the KK-theory of a topological space and the representation theory of the group acting on it. In this article, we review the basics of equivariant KK-theory and focus on the localization theorem and formula due to Atiyah and Segal, which have become important tools in equivariant topology nowadays. We then discuss the application of equivariant KK-theory to equivariant formality, and briefly mention some recent developments.

Keywords

Cite

@article{arxiv.2306.06951,
  title  = {A stroll in equivariant $K$-theory},
  author = {Chi-Kwong Fok},
  journal= {arXiv preprint arXiv:2306.06951},
  year   = {2023}
}

Comments

Expository article, 22 pages. Only some changes in formatting were made. To appear in Contemporary Mathematics

R2 v1 2026-06-28T11:02:41.613Z