A combinatorial model for the teichmüller metric

Abstract

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. © 2007 Birkhäuser Verlag, Basel.