It is a long-standing question whether a group of type F that does not contain Baumslag–Solitar subgroups is necessarily hyperbolic. One-relator groups are of type F and Louder and Wilton showed that if the defining relator has imprimitivity rank greater than 2, they do not contain Baumslag-Solitar subgroups, so they conjecture that such groups are hyperbolic. Cashen and I verified the conjecture computationally for relators of length at most 17. In this talk I’ll introduce hyperbolic groups and the imprimitivity rank of elements in a free group. I’ll also discuss how to verify hyperbolicity using versions of combinatorial curvature on van Kampen diagrams.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
