Hyperfiniteness for group actions on trees
Group Theory
2025-07-10 v2 Logic
Operator Algebras
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.
Cite
@article{arxiv.2307.10964,
title = {Hyperfiniteness for group actions on trees},
author = {Srivatsav Kunnawalkam Elayavalli and Koichi Oyakawa and Forte Shinko and Pieter Spaas},
journal= {arXiv preprint arXiv:2307.10964},
year = {2025}
}
Comments
8 pages; published version