Work

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

Year: 2025

Type: article

Abstract: 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.

Source: Annals of Mathematics

DOI: 10.4007/annals.2025.201.3.4

Authors: Andrei Jaikin-Zapirain, Marco Linton

Institutions: Consejo Superior de Investigaciones Científicas, Institute of Mathematical Sciences, Universidad Carlos III de Madrid, Universidad Autónoma de Madrid

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Instituto de Ciencias Matemáticas, European Commission, Ministerio de Ciencia e Innovación