Mathematics > Group Theory
[Submitted on 18 Jul 2023 (v1), last revised 29 Apr 2024 (this version, v3)]
Title:Relative hyperbolicity of free extensions of free groups
View PDF HTML (experimental)Abstract:We give necessary and sufficient conditions for a free-by-free group to be relatively hyperbolic with a cusp-preserving structure. Namely, if $\phi_1, \ldots , \phi_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 $\phi_i$, 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 $\phi_1, \ldots , \phi_k $, will be hyperbolic.
Submission history
From: Funda Gultepe [view email][v1] Tue, 18 Jul 2023 23:03:31 UTC (60 KB)
[v2] Tue, 19 Dec 2023 12:43:40 UTC (1,312 KB)
[v3] Mon, 29 Apr 2024 18:40:08 UTC (74 KB)
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