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Homology of odometers

Part of: Selfadjoint operator algebras Topological and differentiable algebraic systems

Published online by Cambridge University Press:  13 March 2019

EDUARDO SCARPARO
EDUARDO SCARPARO*
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-970Florianópolis-SC, Brazil email duduscarparo@gmail.com
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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.

Keywords

odometersgroupoid homologyK-theory

MSC classification

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory)
Secondary: 22A22: Topological groupoids (including differentiable and Lie groupoids)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 9 , September 2020 , pp. 2541 - 2551
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Copyright
© Cambridge University Press, 2019

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