Giles Gardam: One-relator groups with no bad subgroups
A group defined by a presentation with only one relator is called a one-relator group. Various conjectures and questions suggested that a one-relator with no subgroup isomorphic to a Baumslag--Solitar group \(BS(m, n)\) for \(m \neq \pm n\) would enjoy various nice geometric properties, such as automaticity and acting freely on CAT(0) cube complexes. In this talk I will introduce examples showing that this is not the case. Joint work with Daniel Woodhouse.
