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arXiv · 2410.09263

On the $K$-theory of groups of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ square-free

Luis Jorge Sánchez Saldaña·Mario Velásquez
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Abstract

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 L\"uck-Davis and Langer-L\"uck.

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Luis Jorge Sánchez Saldaña, Mario Velásquez. 2024-10-11. On the $K$-theory of groups of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ square-free. https://arxiv.org/abs/2410.09263

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