Almost finiteness, comparison, and tracial $\mathcal{Z}$-stability

Liao, Hung-Chang; Tikuisis, Aaron

doi:10.48550/arxiv.2001.10107

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Basics For Amenable Group Actions1

Questions For Further Study1

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2020

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“…We also remark that for amenable group actions on zero-dimensional spaces a result analogous to Proposition 3.2 holds. However, it is not known whether a result about the small boundary property similar to that in [65,66] holds for amenable group actions, even though the small boundary property has been studied for Z k -actions in [44] and for amenable group actions in [56,63] (but we are not going to need this).…”

Section: Basics For Amenable Group Actionsmentioning

confidence: 99%

“…As mentioned in §3, the small boundary property plays an important role in the definition of entropy structure for Z-actions. Small boundary property has been discussed for Z k -actions in [44] and for amenable group actions in [56,63], yet the following question remains open: 28 Problem 9.9. Which G-actions with finite topological entropy admit a refining sequence of finite Borel partitions with small boundaries?…”

Section: Questions For Further Studymentioning

confidence: 99%

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