Graphical small cancellation and hyperfiniteness of boundary actions
arXiv:2509.05548 · doi:10.1112/jlms.70516
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.
17 pages, 12 figures. Comments welcome. Final version accepted to Journal of the London Mathematical Society