Hyperfiniteness for group actions on trees

2023/07/20 by Elayavalli, Srivatsav Kunnawalkam, Oyakawa, Koichi, Shinko, Forte +1
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2307.10964

Abstract

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.

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