Acylindrical Hyperbolicity of Subgroups
| Autor: | Pal, Abhijit, Pandey, Rahul |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | New York Journal of Mathematics 26 (2020) 1213-1231 |
| Druh dokumentu: | Working Paper |
| Popis: | Suppose $G$ is a finitely generated group and $H$ is a subgroup of $G$. Let $\partial_{c}^{\mathcal{F}\mathcal{Q}}G$ denote the contracting boundary of $G$ with the topology of fellow travelling quasi-geodesics defined by Cashen-Mackay \cite{cashen2017}. In this article, we show that if the limit set $\Lambda(H)$ of $H$ in $\partial_{c}^{\mathcal{F}\mathcal{Q}}G$ is compact and contains at least three points then the action of the subgroup $H$ on the space of distinct triples $\Theta_{3}(\Lambda(H))$ is properly discontinuous. By applying a result of B. Sun \cite{BinSun}, if the limit set $\Lambda(H)$ is compact and the action of $H$ on $\partial_{c}^{\mathcal{F}\mathcal{Q}}G$ is non-elementary then $H$ becomes an acylindrically hyperbolic group Comment: Minor errors corrected. Accepted in NYJM |
| Databáze: | arXiv |
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