By the work of Brodzki–Niblo–Nowak–Wright and Monod, topological amenability of a continuous group action can be characterized using uniformly finite homology groups or bounded cohomology groups associated to this action. We show that (certain variations of) these groups are invariants for topologically free actions under continuous orbit equivalence.

中文翻译：

---

连续轨道等价下的上同调群不变

通过 Brodzki–Niblo–Nowak–Wright 和 Monod 的工作，连续群作用的拓扑顺从性可以使用与该作用相关的一致有限同调群或有界上同调群来表征。我们表明，这些组（的某些变体）是连续轨道等价下拓扑自由动作的不变量。