Geodesic
A characterization of short curves of a Teichmüller geodesic
Rafi, Kasra1
1 Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, USA
Geometry & topology, Tome 9 (2005) no. 1, pp. 179-202.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We provide a combinatorial condition characterizing curves that are short along a Teichmüller geodesic. This condition is closely related to the condition provided by Minsky for curves in a hyperbolic 3–manifold to be short. We show that short curves in a hyperbolic manifold homeomorphic to S×ℝ are also short in the corresponding Teichmüller geodesic, and we provide examples demonstrating that the converse is not true.

DOI : 10.2140/gt.2005.9.179
Keywords: Teichmüller space, geodesic, short curves, complex of curves, Kleinian group, bounded geometry

Rafi, Kasra 1

1 Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, USA 
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Rafi, Kasra. A characterization of short curves of a Teichmüller geodesic. Geometry & topology, Tome 9 (2005) no. 1, pp. 179-202. doi : 10.2140/gt.2005.9.179. http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.179/

[1] J Brock, D Canary, Y Minsky, The classification of Kleinian surface groups II: the ending lamination conjecture, in preparation

[2] Y Minsky, The classification of Kleinian surface groups I: models and bounds

[3] K Rafi, Hyperbolic 3–manifolds and geodesics in Teichmüller space, PhD thesis, SUNY at Stony Brook (2001)

[4] M Rees, The geometric model and large Lipschitz equivalence direct from Teichmüller geodesic, preprint

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