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Almost finiteness and homology of certain non-free actions
We show that Cantor minimal \mathbb{Z}\rtimes\mathbb{Z}_2 -systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal \mathbb{Z}\rtimes\mathbb{Z}_2 -systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.