Louder, Larsen;
Wilton, Henry;
(2021)
Uniform negative immersions and the coherence of one-relator groups.
arXiv
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Abstract
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.
| Type: | Working / discussion paper |
|---|---|
| Title: | Uniform negative immersions and the coherence of one-relator groups |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://doi.org/10.48550/arXiv.2107.08911 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10187626 |
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