A characterization of short curves of a Teichmueller geodesic

Details A characterization of short curves of a Teichmueller geodesic A characterization of short curves of a Teichmueller geodesic

2004-04-12

arxiv.org/abs/math/0404227v3

Geom. Topol. 9(2005) 179-202

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper5.abs.html

Scientific paper

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.

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