eprintid: 10188998 rev_number: 10 eprint_status: archive userid: 699 dir: disk0/10/18/89/98 datestamp: 2024-03-14 08:57:35 lastmod: 2024-03-14 08:57:35 status_changed: 2024-03-14 08:57:35 type: article metadata_visibility: show sword_depositor: 699 creators_name: Louder, L creators_name: Wilton, H title: Uniform negative immersions and the coherence of one-relator groups ispublished: inpress divisions: UCL divisions: B04 divisions: C06 divisions: F59 note: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 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. date: 2024-01-01 date_type: published publisher: Springer Science and Business Media LLC official_url: http://dx.doi.org/10.1007/s00222-024-01246-4 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2257092 doi: 10.1007/s00222-024-01246-4 lyricists_name: Louder, Larsen lyricists_id: LLOUD96 actors_name: Louder, Larsen actors_id: LLOUD96 actors_role: owner full_text_status: public publication: Inventiones Mathematicae issn: 0020-9910 citation: Louder, L; Wilton, H; (2024) Uniform negative immersions and the coherence of one-relator groups. Inventiones Mathematicae 10.1007/s00222-024-01246-4 <https://doi.org/10.1007/s00222-024-01246-4>. (In press). Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10188998/2/Louder_s00222-024-01246-4.pdf