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Homology of odometers

2019; Cambridge University Press; Volume: 40; Issue: 9 Linguagem: Inglês

10.1017/etds.2019.13

1469-4417

Eduardo Scarparo,

Advanced Topics in Algebra

We compute the homology groups of transformation groupoids associated with odometers and show that certain $(\mathbb{Z}\rtimes \mathbb{Z}_{2})$ -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 $C_{r}^{\ast }(G)$ . We also show that transformation groupoids of odometers satisfy the AH conjecture.