Stable Teichmueller quasigeodesics and ending laminations

Abstract

We characterize which cobounded quasigeodesics in the Teichmueller space T of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path gamma in T, we show that gamma is a quasigeodesic with finite Hausdorff distance from some geodesic if and only if the canonical hyperbolic plane bundle over gamma is a hyperbolic metric space. As an application, for complete hyperbolic 3-manifolds N with finitely generated, freely indecomposable fundamental group and with bounded geometry, we give a new construction of model geometries for the geometrically infinite ends of N, a key step in Minsky's proof of Thurston's ending lamination conjecture for such manifolds.

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper2.abs.html

References in corpus (2)

• Convex cocompact subgroups of mapping class groups
• Bounded geometry for Kleinian groups

Cited by in corpus (8)

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• Cannon-Thurston Maps for Kleinian Groups
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• Extensions of Veech groups I: A hyperbolic action
• Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy
• Explicit equivalences between CAT(0) hyperbolic type geodesics