Cohomology and K-theory rings of the space of commuting elements in SU(2)

Chi-Kwong Fok

doi:10.4310/HHA.2025.v27.n2.a6

Cohomology and K-theory rings of the space of commuting elements in SU(2)

Chi-Kwong Fok

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we compute explicitly both the K-theory and integral cohomology rings of the space of commuting elements in SU(2) via the K-theory of its desingularization. We also briefly discuss the different behavior of its cohomology with complex and coefficients in the context of representation stability and FI-modules.

Original language	English
Pages (from-to)	123-149
Journal	Homology, Homotopy and Applications
Volume	27
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2025.v27.n2.a6
Publication status	Published - 15 Oct 2025

Keywords

Cohomology, K-theory, space of commuting elements, FI-module

Access to Document

10.4310/HHA.2025.v27.n2.a6

1 Participating in an event e.g. a conference, workshop, …
1 Invited talk
1 Presentation at conference/workshop/seminar

Topology of the space of commuting elements in SU(2)
Fok, C.-K. (Speaker)
26 Aug 2026
Activity: Talk or presentation › Invited talk
Focus Program on Algebraic Topology in Memory of Fred Cohen
Fok, C.-K. (Participant)
7 Jul 2025 → 1 Aug 2025
Activity: Participating in or organising an event › Participating in an event e.g. a conference, workshop, …
Spaces with symmetry through the K-theoretic lens
Fok, C.-K. (Speaker)
4 Dec 2024
Activity: Talk or presentation › Presentation at conference/workshop/seminar

Cite this

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title = "Cohomology and K-theory rings of the space of commuting elements in SU(2)",

abstract = "In this paper, we compute explicitly both the K-theory and integral cohomology rings of the space of commuting elements in SU(2) via the K-theory of its desingularization. We also briefly discuss the different behavior of its cohomology with complex and coefficients in the context of representation stability and FI-modules.",

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AB - In this paper, we compute explicitly both the K-theory and integral cohomology rings of the space of commuting elements in SU(2) via the K-theory of its desingularization. We also briefly discuss the different behavior of its cohomology with complex and coefficients in the context of representation stability and FI-modules.

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Cohomology and K-theory rings of the space of commuting elements in SU(2)

Abstract

Keywords

Access to Document

Activities

Topology of the space of commuting elements in SU(2)

Focus Program on Algebraic Topology in Memory of Fred Cohen

Spaces with symmetry through the K-theoretic lens

Cite this