Geometry & Topology, Vol. 7 (2003)
Paper no. 2, pages 33--90.
Stable Teichmueller quasigeodesics and ending laminations
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.
Teichmueller space, hyperbolic space, quasigeodesics, ending laminations
AMS subject classification.
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
Deptartment of Mathematics and Computer Science
Rutgers University, Newark, NJ 07102
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