Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology of odometers   We compute the homology groups of transformation groupoids associated with
odometers and show that certain infinite dihedral group odometers give rise to
counterexamples to the HK conjecture, which relates the homology of an
essentially principal, minimal, ample groupoid $G$ with the K-theory of
$C^*_r(G)$. We also show that transformation grupoids of odometers satisfy the
AH conjecture.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con