Bowditch, B. H. (Brian Hayward), 1961- (2010) Coarse hyperbolic models for 3-manifolds. Coventry: University of Warwick. (Unpublished)

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Abstract

We give a characteristion of models of hyperbolic 3-manifolds in terms of Gromov hyperbolicity. Let M be a riemannian manifold with a homotopically equivalence to a closed surface, Sigma, which associates cusps of M to boundary components of Sigma. Under some assumption on M, notably that that universal cover of M is Gromov hyperbolic, we show that the ends of M can be classified as geometrically finite or simply degenerate. To any simply degenerate end we assoicated an ending lamination. We show that any two doubly degenerate manifolds of this sort with the same ending laminations are equivalent, in the sense that their universal covers are equivariantly quasi-isometric. In particular, this applies to constant curvature hyperbolic 3-manifold. A consequence is the ending lamintion conjecture for such manifolds, as proven by Minsky, Brock and Canary.

Item Type:	Scholarly Text
Subjects:	Q Science > QA Mathematics
Publisher:	University of Warwick
Place of Publication:	Coventry
Date:	2010
Number of Pages:	34
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Access rights to Published version:	Open Access
Related URLs:	Publisher
URI:	http://wrap.warwick.ac.uk/id/eprint/48813

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