English

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

R2 v1 2026-07-01T05:24:02.316Z