Hyperfiniteness of boundary actions of relatively hyperbolic groups

  • Chris Karpinski

    McGill University, Montreal, Canada
Hyperfiniteness of boundary actions of relatively hyperbolic groups cover
Download PDF

A subscription is required to access this article.

Abstract

We show that if is a finitely generated group hyperbolic relative to a finite collection of subgroups , then the natural action of on the geodesic boundary of the associated relative Cayley graph induces a hyperfinite equivalence relation. As a corollary of this, we obtain that the natural action of on its Bowditch boundary also induces a hyperfinite equivalence relation. This strengthens a result of Ozawa obtained for consisting of amenable subgroups and uses a recent work of Marquis and Sabok.

Cite this article

Chris Karpinski, Hyperfiniteness of boundary actions of relatively hyperbolic groups. Groups Geom. Dyn. (2024), published online first

DOI 10.4171/GGD/813