Homology of odometers
Copyright policy )Homology of odometers
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.
groupoid homology, $K$-theory, odometers, Mathematics - Operator Algebras, FOS: Mathematics, \(K\)-theory and operator algebras (including cyclic theory), Group Theory (math.GR), HK conjecture, Operator Algebras (math.OA), Mathematics - Group Theory, Topological groupoids (including differentiable and Lie groupoids)
groupoid homology, $K$-theory, odometers, Mathematics - Operator Algebras, FOS: Mathematics, \(K\)-theory and operator algebras (including cyclic theory), Group Theory (math.GR), HK conjecture, Operator Algebras (math.OA), Mathematics - Group Theory, Topological groupoids (including differentiable and Lie groupoids)
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