Suppose is a train track on a surface . Let be the set of isotopy classes of simple closed curves carried by . Masur and Minsky  prove that is quasi-convex inside the curve complex . We prove that the complement, , is quasi-convex.
Cite this article
Vaibhav Gadre, Saul Schleimer, The curves not carried. Groups Geom. Dyn. 10 (2016), no. 4, pp. 1249–1264DOI 10.4171/GGD/382