The curves not carried
- Publisher: European Mathematical Society
QA | 57M99 (Primary), 30F60, 20F65 (Secondary) | Mathematics - Geometric Topology
arxiv: Mathematics::Geometric Topology
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  prove $C(\tau)$ is quasi-convex inside the curve complex $C(S)$. We prove the complement, $C(S) - C(\tau)$, is quasi-convex.