Uniform negative immersions and the coherence of one-relator groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866911773061283840 |
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| author | Louder, Larsen Wilton, Henry |
| author_facet | Louder, Larsen Wilton, Henry |
| contents | Previously, the authors proved that the presentation complex of a one-relator group $G$ satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of $G$ is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to uniform negative immersions, using a rationality theorem proved with linear-programming techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08911 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Uniform negative immersions and the coherence of one-relator groups Louder, Larsen Wilton, Henry Group Theory Geometric Topology Previously, the authors proved that the presentation complex of a one-relator group $G$ satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of $G$ is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to uniform negative immersions, using a rationality theorem proved with linear-programming techniques. |
| title | Uniform negative immersions and the coherence of one-relator groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2107.08911 |