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arXiv · 2604.19154

Hyperbolicity of Multiple Ascending HNN Extensions of Free Groups

SK Kiran Ajij
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Abstract

Bestvina-Feighn-Handel show that for finitely many generic and independent hyperbolic automorphisms $ϕ_1, \cdots, ϕ_r$ of $F_n$, the resulting extension $F_n \rtimes F_r$ is hyperbolic. This paper generalizes the above statement to the case where $ϕ_1, \cdots, ϕ_r$ are hyperbolic non-surjective endomorphisms of $F_n$. In our case the output is a multiple HNN extension associated to a graph with one vertex and $r$ edges. All edge and vertex groups are isomorphic to $F_n$.

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SK Kiran Ajij. 2026-04-21. Hyperbolicity of Multiple Ascending HNN Extensions of Free Groups. https://arxiv.org/abs/2604.19154

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