On the coherence of one-relator groups and their group algebras

• 成果类型: Article
• 署名作者: Jaikin-Zapirain, Andrei; Linton, Marco
• 署名单位: Autonomous University of Madrid; Universidad Carlos III de Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Universidad Carlos III de Madrid; Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT)
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2025.201.3.4
• 发表日期: 2025-05
• 页码: 909-959
• 关键词: one-relator groups; non-positive immersions; L2-Betti numbers; division ring embeddings; coherence; homological coherence; ring coherence; division rings; SUBGROUPS; fractions; PRODUCTS; conjecture; ELEMENTS; torsion; THEOREM

摘要

We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations without proper powers are coherent.