Surface groups among cubulated hyperbolic and one-relator groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912838909427712 |
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| author | Wilton, Henry |
| author_facet | Wilton, Henry |
| contents | Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $π_1(X)$ has a non-free subgroup of infinite index unless $π_1(X)$ is either free or a surface group, answering questions of Gromov and Whyte (in a special case) and Wise. A similar result for one-relator groups follows, answering a question posed by several authors. The proof relies on a careful analysis of free and cyclic splittings of cubulated groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surface groups among cubulated hyperbolic and one-relator groups Wilton, Henry Group Theory Geometric Topology Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $π_1(X)$ has a non-free subgroup of infinite index unless $π_1(X)$ is either free or a surface group, answering questions of Gromov and Whyte (in a special case) and Wise. A similar result for one-relator groups follows, answering a question posed by several authors. The proof relies on a careful analysis of free and cyclic splittings of cubulated groups. |
| title | Surface groups among cubulated hyperbolic and one-relator groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2406.02121 |