#### Geometry & Topology, Vol. 7 (2003)
Paper no. 2, pages 33--90.

## Stable Teichmueller quasigeodesics and ending laminations

### Lee Mosher

**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.
**Keywords**.
Teichmueller space, hyperbolic space, quasigeodesics, ending laminations

**AMS subject classification**.
Primary: 57M50.
Secondary: 32G15.

**DOI:** 10.2140/gt.2003.7.33

**E-print:** `arXiv:math.GT/0107035`

Submitted to GT on 15 November 2001.
(Revised 6 January 2003.)
Paper accepted 31 Januray 2003.
Paper published 1 February 2003.

Notes on file formats
Lee Mosher

Deptartment of Mathematics and Computer Science

Rutgers University, Newark, NJ 07102

Email: mosher@andromeda.rutgers.edu

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