Uniform negative immersions and the coherence of one-relator groups

• 成果类型: Article
• 署名作者: Louder, Larsen; Wilton, Henry
• 署名单位: University of London; University College London; University of Cambridge
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01246-4
• 发表日期: 2024
• 页码: 673-712
• 关键词: SECTIONAL CURVATURE; HYPERBOLIC GROUPS; RIGIDITY; SURFACES

摘要

Previously, the authors proved that the presentation complex of a one-relator group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} 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.