Geometry & Topology 9 (2005) 179–202

DOI: 10.2140/gt.2005.9.179

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

Primary: 30F60

Secondary: 30F40, 32G15, 57M07

References

Forward citations

Publication

Received: 11 May 2004
Accepted: 27 December 2004
Published: 8 January 2005
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Walter Neumann

Authors