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

2022/11/25 by Chi-Kwong Fok, Fok, Chi-Kwong
Mathematics · #55N15 #55N20 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2211.13850

openalex publication_date 2022/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℤ₂ coefficients in the context of representation stability and FI-modules.

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