# The curves not carried

### Vaibhav Gadre

University of Warwick, Coventry, UK### Saul Schleimer

University of Warwick, Coventry, UK

## Abstract

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.

## Cite this article

Vaibhav Gadre, Saul Schleimer, The curves not carried. Groups Geom. Dyn. 10 (2016), no. 4, pp. 1249–1264

DOI 10.4171/GGD/382