The coherence of one-relator groups

Marco Linton, Oxford University
Fine Hall 314

(Joint work with Andrei Jaikin-Zapirain) A group is said to be coherent if all of its finitely generated subgroups are finitely presented. Examples of groups known to be coherent include polycyclic groups, surface groups and fundamental groups of three-manifolds. Unfortunately, it is very easy to come across non-coherent groups as seemingly innocuous groups such as the direct product of two non-abelian free groups contain finitely generated infinitely related subgroups. In this talk I will first discuss a topological approach that can be taken to establish coherence of certain groups and will then explain the homological approach we took to prove that all one-relator groups are coherent.