Hyperbolicity of Multiple Ascending HNN Extensions of Free Groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917425336811520 |
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| author | Ajij, SK Kiran |
| author_facet | Ajij, SK Kiran |
| contents | 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 $F_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19154 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity of Multiple Ascending HNN Extensions of Free Groups Ajij, SK Kiran Group Theory 20F65 (primary), 20E06, 20F67 (secondary) 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 $F_n$. |
| title | Hyperbolicity of Multiple Ascending HNN Extensions of Free Groups |
| topic | Group Theory 20F65 (primary), 20E06, 20F67 (secondary) |
| url | https://arxiv.org/abs/2604.19154 |