Hyperfiniteness for group actions on trees

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the afor...

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Bibliographic Details
Main Authors Elayavalli, Srivatsav Kunnawalkam, Oyakawa, Koichi, Shinko, Forte, Spaas, Pieter
Format Journal Article
LanguageEnglish
Published 20.07.2023
Subjects
Mathematics - Group Theory
Mathematics - Logic
Mathematics - Operator Algebras
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Summary:We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfinitenss of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite.
DOI:10.48550/arxiv.2307.10964