Almost finiteness and homology of certain non-free actions

[摘要] We show that Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_2Z⋊Z2​-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_2Z⋊Z2​-systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.

[学科分类] 神经科学

[关键词] Almost finiteness;groupoid homology