Uniform quasiconvexity of the disc graphs in the curve graphs

Abstract

We give a proof that there exists a universal constant $K$ such that the disc graph associated to a surface $S$ forming a boundary component of a compact, orientable 3-manifold $M$ is $K$-quasiconvex in the curve graph of $S$. Our proof does not require the use of train tracks.

8 pages, 3 figures