Geometry & Topology, Vol. 9 (2005) Paper no. 5, pages 179--202.

A characterization of short curves of a Teichmueller geodesic

Kasra Rafi

Abstract. We provide a combinatorial condition characterizing curves that are short along a Teichmueller 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 x R are also short in the corresponding Teichmueller geodesic, and we provide examples demonstrating that the converse is not true.

Keywords. Teichmueller space, geodesic, short curves, complex of curves, Kleinian group, bounded geometry

AMS subject classification. Primary: 30F60. Secondary: 32G15, 30F40, 57M07 .

DOI: 10.2140/gt.2005.9.179

E-print: arXiv:math.GT/0404227

Submitted to GT on 11 May 2004. Paper accepted 27 December 2004. Paper published 8 January 2005.

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Kasra Rafi
Department of Mathematics, University of Connecticut
Storrs, CT 06269, USA

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