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G&T Monographs |
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A characterization of short curves of a Teichmüller
geodesic
Kasra Rafi
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Geometry & Topology 9 (2005)
179–202
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Abstract
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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.
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Keywords
Teichmüller space, geodesic, short
curves, complex of curves, Kleinian group, bounded
geometry
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Mathematical Subject Classification
Primary: 30F60
Secondary: 30F40, 32G15, 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
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