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Homology of odometers
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 9 / September 2020
- Published online by Cambridge University Press:
- 13 March 2019, pp. 2541-2551
- Print publication:
- September 2020
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- Article
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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.
