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arxiv: math/0404227 · v3 · pith:I5UOYCGWnew · submitted 2004-04-12 · 🧮 math.GT

A characterization of short curves of a Teichmueller geodesic

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keywords shortcurvesconditiongeodesicteichmuellerhyperbolicmanifoldalong
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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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