Train track maps and CTs on graphs of groups

Abstract: A train track map is a self-map of a graph with particularly nice properties. Train track maps and their cousins, relative train track maps, were developed by Bestvina and Handel in 1992 to prove the Scott conjecture: the fixed subgroup of an automorphism of a finite-rank free group has rank bounded by the rank of the free group. Since then, relative train track maps, particularly in their modern incarnation as CTs, have become perhaps the main tool in studying outer automorphisms of free groups. We will meet (relative) train track maps and describe a generalization of them to graphs of groups. As an application, we will see an index inequality implying a version of the Scott conjecture for automorphisms of free products.