A characterization of short curves of a Teichmüller geodesic

Abstract

We provide a combinatorial condition characterizing curves that are short along a Teichmüller geodesic. This condition is closely related to the condition provided by Minsky for curves in a hyperbolic 3-manifold to be short. We show that short curves in a hyperbolic manifold homeomorphic to S × ℝ are also short in the corresponding Teichmüller geodesic, and we provide examples demonstrating that the converse is not true.