The curves not carried

Vaibhav Gadre, Saul Schleimer

Published 2014-10-17Version 1

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 complementary set $C(S) - C(\tau)$ is also quasi-convex.