Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911215443247104 |
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| author | Fok, Chi-Kwong |
| author_facet | Fok, Chi-Kwong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13850 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$ Fok, Chi-Kwong Algebraic Topology K-Theory and Homology 55N20, 55N15 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. |
| title | Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$ |
| topic | Algebraic Topology K-Theory and Homology 55N20, 55N15 |
| url | https://arxiv.org/abs/2211.13850 |