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arXiv · 2111.04013

Long exact sequences of homology groups of \'etale groupoids

Hiroki Matui
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Abstract

When a pair of \'etale groupoids $\mathcal{G}$ and $\mathcal{G}'$ on totally disconnected spaces are related in some way, we discuss the difference of their homology groups. More specifically, we treat two basic situations. In the subgroupoid situation, $\mathcal{G}'$ is assumed to be an open regular subgroupoid of $\mathcal{G}$. In the factor groupoid situation, we assume that $\mathcal{G}'$ is a quotient of $\mathcal{G}$ and the factor map $\mathcal{G}\to\mathcal{G}'$ is proper and regular. For each, we show that there exists a long exact sequence of homology groups. We present examples which arise from SFT groupoids and hyperplane groupoids.

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Hiroki Matui. 2021-11-07. Long exact sequences of homology groups of \'etale groupoids. https://arxiv.org/abs/2111.04013

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