We show that the subsurface projection of a train track splitting sequence is
an unparameterized quasi-geodesic in the curve complex of the subsurface. For
the proof we introduce induced tracks, efficient position, and wide curves.
This result is an important step in the proof that the disk complex is Gromov
hyperbolic. As another application we show that train track sliding and
splitting sequences give quasi-geodesics in the train track graph, generalizing
a result of Hamenstaedt [Invent. Math.].Comment: 40 pages, 12 figure
