Hyperfiniteness of boundary actions of relatively hyperbolic groups
Chris Karpinski
McGill University, Montreal, Canada
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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