Relative hyperbolicity of free extensions of free groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914000075227136 |
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| author | Ghosh, Pritam Gültepe, Funda |
| author_facet | Ghosh, Pritam Gültepe, Funda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09674 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative hyperbolicity of free extensions of free groups Ghosh, Pritam Gültepe, Funda Group Theory Geometric Topology 20F65, 20Exx, 20Fxx, 57Mxx 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. |
| title | Relative hyperbolicity of free extensions of free groups |
| topic | Group Theory Geometric Topology 20F65, 20Exx, 20Fxx, 57Mxx |
| url | https://arxiv.org/abs/2307.09674 |