A Combinatorial Model for the Teichmüller Metric

By Kasra Rafi. 2005

100 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47bb6acf9b0c9328e1a32721b74299077f1d8c15

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Kasra Rafi
2. U. Hamenstaedt
3. Samuel J. Taylor

In Geometry and Topology

1. Kasra Rafi
2. Samuel J. Taylor
3. U. Hamenstaedt
4. Saul Schleimer

In Mathematical Physics

1. Kasra Rafi
2. U. Hamenstaedt

Citations in the corpus

• THICK-THIN DECOMPOSITION FOR QUADRATIC DIFFERENTIALS (2014, background): “On the other hand, by the uniformization theorem, there also exists a canonical hyperbolic metric σ in the conformal class of q and the problem of understanding the relationship between the two metrics often arises (see for example [Min92], [Raf05b] and [Raf05a]).”
• Hyperbolicity in Teichmüller space (2010, background): “(See Rafi [15; 16; 17], Choi, Rafi and Series [3].”
• The geometry of right angled Artin subgroups of mapping class groups (2010, unknown): “The analogous result for the Teichmüller metric was proven by Rafi in [38].”