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arXiv · 2512.05293

Largest acylindrical actions of free-by-cyclic groups

Monika Kudlinska·Harry Petyt
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Abstract

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.

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Monika Kudlinska, Harry Petyt. 2025-12-04. Largest acylindrical actions of free-by-cyclic groups. https://arxiv.org/abs/2512.05293

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