Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long exact sequences of homology groups of \'etale groupoids   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 with 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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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ