Profinite non-rigidity of braid groups and free-by-cyclic groups

Abstract: When is a finitely generated algebraic object determined by its finite quotients? This is the core question underlying profinite rigidity. I will give an introduction to some of the key ideas behind profinite rigidity, and discuss some recent results concerning the non-rigidity of some groups. In particular, I will show that braid groups are not profinitely rigid, giving the first known examples of profinitely non-rigid mapping class groups. I will also give a brief overview of a recent result that free-by-cyclic groups are not relatively profinitely rigid, which answered a question of Bridson & Reid from 2015. Time permitting I will also discuss what happens in the semigroup setting, especially for free semigroups.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.