Largest acylindrical actions of free-by-cyclic groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918233369477120 |
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| author | Kudlinska, Monika Petyt, Harry |
| author_facet | Kudlinska, Monika Petyt, Harry |
| contents | We show that every finitely generated free-by-cyclic group $G$ admits a largest acylindrical action on a hyperbolic space $X$ obtained by coning off maximal product subgroups of $G$. We characterise Morse geodesics of $G$ as those that project to quasigeodesics in $X$, thus showing that all finitely generated free-by-cyclic groups are Morse local-to-global. We also characterise the stable and strongly quasiconvex subgroups of $G$. Finally, we compute the Morse boundary for \{finitely generated free\}-by-cyclic groups with unipotent and polynomially growing monodromy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Largest acylindrical actions of free-by-cyclic groups Kudlinska, Monika Petyt, Harry Group Theory Metric Geometry 20F67, 20E22, 57M07 We show that every finitely generated free-by-cyclic group $G$ admits a largest acylindrical action on a hyperbolic space $X$ obtained by coning off maximal product subgroups of $G$. We characterise Morse geodesics of $G$ as those that project to quasigeodesics in $X$, thus showing that all finitely generated free-by-cyclic groups are Morse local-to-global. We also characterise the stable and strongly quasiconvex subgroups of $G$. Finally, we compute the Morse boundary for \{finitely generated free\}-by-cyclic groups with unipotent and polynomially growing monodromy. |
| title | Largest acylindrical actions of free-by-cyclic groups |
| topic | Group Theory Metric Geometry 20F67, 20E22, 57M07 |
| url | https://arxiv.org/abs/2512.05293 |