Almost finiteness and homology of certain non-free actions (Q2694824)

Summary: 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.