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Homology of odometers

Published online by Cambridge University Press:  13 March 2019

EDUARDO SCARPARO*
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-970Florianópolis-SC, Brazil email [email protected]

Abstract

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.

Type
Original Article
Copyright
© Cambridge University Press, 2019

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