Graphical small cancellation and hyperfiniteness of boundary actions
Group Theory
2025-09-09 v1 Logic
Abstract
We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned-off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented) classical small cancellation groups, admit hyperfinite boundary actions, more precisely, the orbit equivalence relation that they induce on the boundaries of the coned-off Cayley graphs is hyperfinite.
Keywords
Cite
@article{arxiv.2509.05548,
title = {Graphical small cancellation and hyperfiniteness of boundary actions},
author = {Chris Karpinski and Damian Osajda and Koichi Oyakawa},
journal= {arXiv preprint arXiv:2509.05548},
year = {2025}
}
Comments
17 pages, 12 figures. Comments welcome