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.
Howard Masur. Lee Mosher. Saul Schleimer. "On train-track splitting sequences." Duke Math. J. 161 (9) 1613 - 1656, 15 June 2012. https://doi.org/10.1215/00127094-1593344