The shadow of a Thurston geodesic to the curve graph

Abstract

We study the geometry of the Thurston metric on Teichmuller space by examining its geodesics and comparing them to Teichmuller geodesics. We show that, similar to a Teichmuller geodesic, the shadow of a Thurston geodesic to the curve graph is a reparametrized quasi-geodesic. However, we show that the set of short curves along the two geodesics are not identical.

34 pages, 10 figures, minor revisions, final version appears in Journal of Topology

References in corpus (2)

• Maximally stretched laminations on geometrically finite hyperbolic manifolds
• Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

Cited by in corpus (7)

• Geodesics in the mapping class group
• Coarse and fine geometry of the Thurston metric
• Generalized stretch lines for surfaces with boundary
• Local Rigidity of Teichmüller space with Thurston metric
• Optimal Lipschitz Maps on One-holed Tori and the Thurston Metric Theory of Teichmueller Space
• Ideal triangles, hyperbolic surfaces and the Thurston metric on Teichm{ü}ller space
• Minimal stretch maps between Euclidean triangle?