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arXiv · 2307.09674

Relative hyperbolicity of free extensions of free groups

Pritam Ghosh·Funda Gültepe
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Abstract

We give necessary and sufficient conditions for a free-by-free group to be relatively hyperbolic with a cusp-preserving structure. Namely, if $ϕ_1, \ldots , ϕ_k $ is a collection of exponentially growing outer automorphisms with a common invariant \emph{subgroup system} such that any conjugacy class in the complement of this system grows exponentially under iteration by all $ϕ_i$, then such a subgroup system can be used to construct a collection of peripheral subgroups relative to which, the extension of $\mathbb F$ by the free group generated by sufficiently high powers of $ϕ_1, \ldots , ϕ_k $, will be hyperbolic.

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Pritam Ghosh, Funda Gültepe. 2025-08-21. Relative hyperbolicity of free extensions of free groups. https://arxiv.org/abs/2307.09674

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