Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
Forum of Mathematics, Sigma, Tome 12 (2024)
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We prove that, for any countable acylindrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph $\Gamma (G,S)$ is hyperbolic, $|\partial \Gamma (G,S)|>2$, the natural action of G on $\Gamma (G,S)$ is acylindrical and the natural action of G on the Gromov boundary $\partial \Gamma (G,S)$ is hyperfinite. This result broadens the class of groups that admit a non-elementary acylindrical action on a hyperbolic space with a hyperfinite boundary action.
@article{10_1017_fms_2024_24,
author = {Koichi Oyakawa},
title = {Hyperfiniteness of boundary actions of acylindrically hyperbolic groups},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2024.24},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.24/}
}
Koichi Oyakawa. Hyperfiniteness of boundary actions of acylindrically hyperbolic groups. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.24
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