JournalsggdVol. 10, No. 4pp. 1249–1264

The curves not carried

  • Vaibhav Gadre

    University of Warwick, Coventry, UK
  • Saul Schleimer

    University of Warwick, Coventry, UK
The curves not carried cover
Download PDF

Abstract

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