The curves not carried

Abstract

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

arXiv comment12 pages, 9 figures. Improved exposition in Section 2. Fixed a mistake in the proof of Lemma 5.4