Groups, Geometry, and Dynamics

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Volume 10, Issue 4, 2016, pp. 1249–1264
DOI: 10.4171/GGD/382

Published online: 2017-01-26

The curves not carried

Vaibhav Gadre[1] and Saul Schleimer[2]

(1) University of Warwick, Coventry, UK
(2) University of Warwick, Coventry, UK

Suppose $\tau$ is a train track on a surface $S$. Let $\mathcal C(\tau)$ be the set of isotopy classes of simple closed curves carried by $\tau$. Masur and Minsky [2004] prove that $\mathcal C(\tau)$ is quasi-convex inside the curve complex $\mathcal C(S)$. We prove that the complement, $\mathcal C(S) - \mathcal C(\tau)$, is quasi-convex.

Keywords: Train tracks, curve complex, quasi-convex

Gadre Vaibhav, Schleimer Saul: The curves not carried. Groups Geom. Dyn. 10 (2016), 1249-1264. doi: 10.4171/GGD/382