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A characterization of short curves of a Teichmuller geodesic

- Kasra Rafi
- Mathematics
- 12 April 2004

We provide a combinatorial condition characterizing curves that are short along a Teichmuller geodesic. This condition is closely related to the condition pro- vided by Minsky for curves in a… Expand

Large scale geometry of big mapping class groups

- Kathryn Mann, Kasra Rafi
- Mathematics
- 23 December 2019

We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete… Expand

A Combinatorial Model for the Teichmüller Metric

- Kasra Rafi
- Mathematics
- 24 September 2005

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… Expand

Comparison between Teichmüller and Lipschitz metrics

- Young-Eun Choi, Kasra Rafi
- Mathematics
- 7 October 2005

We study the Lipschitz metric on a Teichmüller space (defined by Thurston) and compare it with the Teichmüller metric. We show that in the thin part of the Teichmüller space the Lipschitz metric is… Expand

Uniform hyperbolicity of the curve graph via surgery sequences

- Matt Clay, Kasra Rafi, S. Schleimer
- Mathematics
- 22 February 2013

We prove that the curve graph C (1) (S) is Gromov- hyperbolic with a constant of hyperbolicity independent of the surface S. The proof is based on the proof of hyperbolicity of the free splitting… Expand

Length spectra and degeneration of flat metrics

- M. Duchin, C. Leininger, Kasra Rafi
- Mathematics
- 13 July 2009

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves… Expand

Isomorphisms between big mapping class groups

- Juliette Bavard, S. Dowdall, Kasra Rafi
- Mathematics
- 28 August 2017

We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms… Expand

Covers and curve complex

- Kasra Rafi, S. Schleimer
- Mathematics
- 25 January 2007

We provide the first nontrivial examples of quasi-isometric embeddings between curve complexes; these are induced by orbifold covers. This leads to new quasi-isometric embeddings between mapping… Expand

On hyperbolicity of free splitting and free factor complexes

- Ilya Kapovich, Kasra Rafi
- Mathematics
- 16 June 2012

We show how to derive hyperbolicity of the free factor complex of $F_N$ from the Handel-Mosher proof of hyperbolicity of the free splitting complex of $F_N$, thus obtaining an alternative proof of a… Expand

Counting closed geodesics in strata

- A. Eskin, M. Mirzakhani, Kasra Rafi
- MathematicsInventiones mathematicae
- 25 June 2012

We compute the asymptotic growth rate of the number $$N({{\mathcal {C}}}, R)$$N(C,R) of closed geodesics of length $$\le R$$≤R in a connected component $${{\mathcal {C}}}$$C of a stratum of quadratic… Expand

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