Rylee Lyman (Rutgers), `Train track maps and CTs on graphs of groups'

Abstract: A homotopy equivalence of a graph is a train track map when it sends vertices to vertices and the restriction of any iterate of the map to an edge yields an immersion. (Relative) train track maps were introduced by Bestvina and Handel in 1992; since then they have become one of the main tools in the study of outer automorphisms of free groups. More recently in 2011, Feighn and Handel introduced a stronger kind of relative train track map called a CT and proved their existence for all outer automorphisms after passing to a power. We extend the theory of relative train track maps to graphs of groups with finitely generated, co-Hopfian edge groups and the theory of CTs to free products (that is, graphs of groups with trivial edge groups).