CTs for free products

Rylee Lyman (Rutgers)

Abstract: Introduced by Feighn and Handel, a CT is a kind of "dynamical normal form" for an outer automorphism of a finite-rank free group, inspired by the Nielsen–Thurston classification of elements of the mapping class group of a finite-type surface. Recently I constructed CTs for outer automorphisms of free products preserving a free product decomposition. In this talk I'll aim to describe the usefulness of a dynamical normal form, why one would naturally turn from free groups to free products, and how the situation changes from one to the other.