Geometry and Topology Seminar
We will discuss a new approach to determine the minimal quotients of groups of geometric interest, primarily focussing on the Artin braid groups. There were conjectures due to Zimmermann, Mecchia-Zimmermann, and Margalit, for the cases of mapping class groups, outer automorphism groups of free groups, and braid groups respectively. The first two conjectures were proved by Kielak-Pierro, and Baumeister-Kielak-Pierro respectively, and several recent results show support for the conjecture of Margalit. We will outline these approaches, and then describe how the novel inductive orbit-stabilizer method can be used to resolve these conjectures.