Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A characterization of short curves of a Teichmüller geodesic

Kasra Rafi

Geometry & Topology 9 (2005) 179–202

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× 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