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A Combinatorial Model for the Teichmüller Metric

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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.

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  1. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois, 60637, USA

    Kasra Rafi

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  1. Kasra Rafi
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Correspondence to Kasra Rafi.

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Received: October 2005 Revision: April 2006 Accepted: May 2006

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Rafi, K. A Combinatorial Model for the Teichmüller Metric. GAFA, Geom. funct. anal. 17, 936–959 (2007). https://doi.org/10.1007/s00039-007-0615-x

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  • DOI: https://doi.org/10.1007/s00039-007-0615-x

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