The shadow of a Thurston geodesic to the curve graph

Anna Lenzhen (1) , Kasra Rafi (2) , Jing Tao (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics, University of Toronto
3 OU - University of Oklahoma

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.

Domaines: Topologie géométrique [math.GT]

Anna Lenzhen, Kasra Rafi, Jing Tao. The shadow of a Thurston geodesic to the curve graph. Journal of topology, 2015, 8 (4), pp.1085-1118. ⟨10.1112/jtopol/jtv031⟩. ⟨hal-01044489⟩