#### Volume 9, issue 1 (2005)

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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 $S×ℝ$ 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