Geodesic
Hyperfiniteness of boundary actions of relatively hyperbolic groups
Chris Karpinski1 orcid
1McGill University, Montreal, Canada
Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1479-1497

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DOI

We show that if G is a finitely generated group hyperbolic relative to a finite collection of subgroups P, then the natural action of G 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 G on its Bowditch boundary ∂(G,P) also induces a hyperfinite equivalence relation. This strengthens a result of Ozawa obtained for P consisting of amenable subgroups and uses a recent work of Marquis and Sabok.
DOI : 10.4171/ggd/813
Classification : 20F67, 20F65, 03E15
Mots-clés : hyperfinite equivalence relations, relatively hyperbolic groups, Bowditch boundary

Chris Karpinski  1

1 McGill University, Montreal, Canada 
Chris Karpinski. Hyperfiniteness of boundary actions of relatively hyperbolic groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1479-1497. doi: 10.4171/ggd/813
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     title = {Hyperfiniteness of boundary actions of relatively hyperbolic groups},
     journal = {Groups, geometry, and dynamics},
     pages = {1479--1497},
     year = {2025},
     volume = {19},
     number = {4},
     doi = {10.4171/ggd/813},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/813/}
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