A Combinatorial Model for the Teichmüller Metric

We study how the length and the twisting parameter of a curve change along a Teichmüller geodesic. We then use our results to provide a formula for the Teichmüller distance between two hyperbolic metrics on a surface, in terms of the combinatorial complexity of curves of bounded lengths in these two metrics. Received: October 2005 Revision: April 2006 Accepted: May 2006