On train track splitting sequences

Details On train track splitting sequences On train track splitting sequences

2010-04-26

arxiv.org/abs/1004.4564v1

Mathematics

Geometric Topology

40 pages, 12 figures

Scientific paper

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.].

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