On the $K$-theory of groups of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ square-free
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913543175012352 |
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| author | Saldaña, Luis Jorge Sánchez Velásquez, Mario |
| author_facet | Saldaña, Luis Jorge Sánchez Velásquez, Mario |
| contents | We provide an explicit computation of the topological $K$-theory groups $K_*(C_r^*(\mathbb{Z}^n\rtimes \mathbb{Z}/m))$ of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}Z/m$ with $m$ square-free. We want to highlight the fact that we are not impossing any conditions on the $\Z/m$-action on $\mathbb{Z}^n$. This generalizes previous computations of Lück-Davis and Langer-Lück. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $K$-theory of groups of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ square-free Saldaña, Luis Jorge Sánchez Velásquez, Mario K-Theory and Homology We provide an explicit computation of the topological $K$-theory groups $K_*(C_r^*(\mathbb{Z}^n\rtimes \mathbb{Z}/m))$ of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}Z/m$ with $m$ square-free. We want to highlight the fact that we are not impossing any conditions on the $\Z/m$-action on $\mathbb{Z}^n$. This generalizes previous computations of Lück-Davis and Langer-Lück. |
| title | On the $K$-theory of groups of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ square-free |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2410.09263 |