On train-track splitting sequences

Abstract

We present a structure theorem for the subsurface projections of train-track splitting sequences. For the proof we introduce induced tracks, efficient position, and wide curves. As a consequence of the structure theorem, we prove that train-track sliding and splitting sequences give quasi-geodesics in the train-track graph; this generalizes a result of Hamenstädt. © 2012 by Howard Masur, LeeMosher, and Saul Schleimer.