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arXiv · 2211.13850

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

Chi-Kwong Fok
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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 $\mathbb{Z}_2$ coefficients in the context of representation stability and FI-modules.

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Chi-Kwong Fok. 2022-11-25. Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$. https://doi.org/10.4310/hha.2025.v27.n2.a6

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