A characterization of short curves of a Teichmüller geodesic

Rafi, Kasra

doi:10.2140/gt.2005.9.179

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A characterization of short curves of a Teichmüller geodesic

Kasra Rafi

Geometry & Topology 9 (2005) 179–202

DOI: 10.2140/gt.2005.9.179

arXiv: math.GT/0404227

Abstract

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 $S \times ℝ$ are also short in the corresponding Teichmüller geodesic, and we provide examples demonstrating that the converse is not true.

Keywords

Teichmüller space, geodesic, short curves, complex of curves, Kleinian group, bounded geometry

Mathematical Subject Classification 2000

Primary: 30F60

Secondary: 32G15, 30F40, 57M07

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Publication

Received: 11 May 2004

Accepted: 27 December 2004

Published: 8 January 2005

Proposed: Benson Farb

Seconded: Jean-Pierre Otal, Walter Neumann

Authors

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

Volume 9, issue 1 (2005)