#### Volume 7, issue 1 (2003)

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Stable Teichmüller quasigeodesics and ending laminations

### Lee Mosher

Geometry & Topology 7 (2003) 33–90
 arXiv: math.GT/0107035
##### Abstract

We characterize which cobounded quasigeodesics in the Teichmüller space $\mathsc{T}$ of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path $\gamma$ in $\mathsc{T}$, 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.

##### Keywords
Teichmüller space, hyperbolic space, quasigeodesics, ending laminations
Primary: 57M50
Secondary: 32G15
##### Publication
Received: 15 November 2001
Revised: 6 January 2003
Accepted: 31 2003
Published: 1 February 2003
Proposed: Walter Neumann
Seconded: Benson Farb, David Gabai
##### Authors
 Lee Mosher Department of Mathematics and Computer Science Rutgers University Newark New Jersey 07102 USA