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arXiv · 2307.10964

Hyperfiniteness for group actions on trees

Srivatsav Kunnawalkam Elayavalli·Koichi Oyakawa·Forte Shinko·Pieter Spaas
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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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Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko, Pieter Spaas. 2023-07-20. Hyperfiniteness for group actions on trees. https://doi.org/10.1090/proc%2F16851

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