A stroll in equivariant K-theory

Chi-Kwong Fok

doi:10.1090/conm/808/16181

A stroll in equivariant K-theory

Chi-Kwong Fok^*

^*Corresponding author for this work

Department of Pure Mathematics

NYU-ECNU Institute of Mathematical Sciences, New York University Shanghai

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

Abstract

Equivariant K-theory is a generalized equivariant cohomology theory that is a hybrid of the K-theory of a topological space and the representation theory of a group acting on it. In this article, we review the basics of equivariant K-theory and focus on the localization theorem of 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.

Original language	English
Title of host publication	Proceedings of the Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting
Editors	Loring W. Tu
Publisher	American Mathematical Society
Pages	79-101
Number of pages	23
ISBN (Print)	9781470471804
DOIs	https://doi.org/10.1090/conm/808/16181
Publication status	Published - 2024
Event	Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting, 2022 - Virtual, Online Duration: 19 Mar 2022 → 20 Mar 2022

Publication series

Name	Contemporary Mathematics
Volume	808
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting, 2022
City	Virtual, Online
Period	19/03/22 → 20/03/22

Keywords

Atiyah–Segal localization formula
equivariant formality
Equivariant K-theory
Segal localization theorem
twisted K-theory

Access to Document

10.1090/conm/808/16181

Cite this

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title = "A stroll in equivariant K-theory",

abstract = "Equivariant K-theory is a generalized equivariant cohomology theory that is a hybrid of the K-theory of a topological space and the representation theory of a group acting on it. In this article, we review the basics of equivariant K-theory and focus on the localization theorem of 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.",

keywords = "Atiyah–Segal localization formula, equivariant formality, Equivariant K-theory, Segal localization theorem, twisted K-theory",

author = "Chi-Kwong Fok",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society.; Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting, 2022 ; Conference date: 19-03-2022 Through 20-03-2022",

year = "2024",

doi = "10.1090/conm/808/16181",

language = "English",

isbn = "9781470471804",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "79--101",

editor = "Tu, {Loring W.}",

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Fok, C-K 2024, A stroll in equivariant K-theory. in LW Tu (ed.), Proceedings of the Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting. Contemporary Mathematics, vol. 808, American Mathematical Society, pp. 79-101, Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting, 2022, Virtual, Online, 19/03/22. https://doi.org/10.1090/conm/808/16181

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N2 - Equivariant K-theory is a generalized equivariant cohomology theory that is a hybrid of the K-theory of a topological space and the representation theory of a group acting on it. In this article, we review the basics of equivariant K-theory and focus on the localization theorem of 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.

AB - Equivariant K-theory is a generalized equivariant cohomology theory that is a hybrid of the K-theory of a topological space and the representation theory of a group acting on it. In this article, we review the basics of equivariant K-theory and focus on the localization theorem of 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.

KW - Atiyah–Segal localization formula

KW - equivariant formality

KW - Equivariant K-theory

KW - Segal localization theorem

KW - twisted K-theory

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U2 - 10.1090/conm/808/16181

DO - 10.1090/conm/808/16181

M3 - Conference Proceeding

AN - SCOPUS:85213374957

SN - 9781470471804

T3 - Contemporary Mathematics

SP - 79

EP - 101

BT - Proceedings of the Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting

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T2 - Special Session on Equivariant Cohomology of the AMS Eastern Sectional Meeting, 2022

Y2 - 19 March 2022 through 20 March 2022

ER -

A stroll in equivariant K-theory

Abstract

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