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

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