Title of Seminar: Random Geometry Seminar 2025
Title of Talk: Train tracks and automorphisms of free groups
Speaker: Amartya Muthal, TIFR, Mumbai
Date: April 02, 2024
Time: 15:30:00 Hours
Venue: A-369

Abstract: On a surface $S$, a measured train track is a combinatorial tool that allows us to assign coordinates to isotopy classes of essential simple closed curves. This allows us to see the action of a diffeomorphism on curves in terms of linear algebra on train tracks. In the context of free group automorphisms, this takes the form of finding an efficient representative of an automorphism as a nice homotopy equivalence of graphs, called a train track map. In this talk, I will introduce the idea of train track maps and show how a generalisation of it, called relative train track maps, was used to prove Scott's conjecture: Fixed subgroups of automorphisms of $F_n$ have rank at most $n$.