Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914948903337984 |
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| author | Oyakawa, Koichi |
| author_facet | Oyakawa, Koichi |
| contents | We prove that for any countable acylidrically hyperbolic group $G$, there exists a generating set $S$ of $G$ such that the corresponding Cayley graph $Γ(G,S)$ is hyperbolic, $|\partialΓ(G,X)|>2$, the natural action of $G$ on $Γ(G,S)$ is acylindrical, and the natural action of $G$ on the Gromov boundary $\partialΓ(G,S)$ is hyperfinite. This result broadens a class of groups that admit a non-elementary acylindrical action on a hyperbolic space with hyperfinite boundary action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09790 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperfiniteness of boundary actions of acylindrically hyperbolic groups Oyakawa, Koichi Group Theory Logic We prove that for any countable acylidrically hyperbolic group $G$, there exists a generating set $S$ of $G$ such that the corresponding Cayley graph $Γ(G,S)$ is hyperbolic, $|\partialΓ(G,X)|>2$, the natural action of $G$ on $Γ(G,S)$ is acylindrical, and the natural action of $G$ on the Gromov boundary $\partialΓ(G,S)$ is hyperfinite. This result broadens a class of groups that admit a non-elementary acylindrical action on a hyperbolic space with hyperfinite boundary action. |
| title | Hyperfiniteness of boundary actions of acylindrically hyperbolic groups |
| topic | Group Theory Logic |
| url | https://arxiv.org/abs/2307.09790 |