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2003 Stable Teichmüller quasigeodesics and ending laminations
Lee Mosher
Geom. Topol. 7(1): 33-90 (2003). DOI: 10.2140/gt.2003.7.33

Abstract

We characterize which cobounded quasigeodesics in the Teichmüller space T of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path γ in T, we show that γ is a quasigeodesic with finite Hausdorff distance from some geodesic if and only if the canonical hyperbolic plane bundle over γ 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.

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Lee Mosher. "Stable Teichmüller quasigeodesics and ending laminations." Geom. Topol. 7 (1) 33 - 90, 2003. https://doi.org/10.2140/gt.2003.7.33

Information

Received: 15 November 2001; Revised: 6 January 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1021.57009
MathSciNet: MR1988281
Digital Object Identifier: 10.2140/gt.2003.7.33

Subjects:
Primary: 57M50
Secondary: 32G15

Rights: Copyright © 2003 Mathematical Sciences Publishers

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