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arXiv · 2306.06951

A stroll in equivariant $K$-theory

Chi-Kwong Fok
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Abstract

Equivariant $K$-theory is a generalized equivariant cohomology theory which is a hybrid of the $K$-theory of a topological space and the representation theory of the group acting on it. In this article, we review the basics of equivariant $K$-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 $K$-theory to equivariant formality, and briefly mention some recent developments.

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Chi-Kwong Fok. 2023-06-12. A stroll in equivariant $K$-theory. https://arxiv.org/abs/2306.06951

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