Hyperfiniteness for group actions on trees

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.

arXiv comment8 pages; published version

References in corpus (4)

• Hyperfiniteness of boundary actions of cubulated hyperbolic groups
• Hyperfiniteness of boundary actions of hyperbolic groups
• Unicorn paths and hyperfiniteness for the mapping class group
• Hyperfiniteness of boundary actions of acylindrically hyperbolic groups