The classification of Kleinian surface groups, I: Models and bounds

Mathematics – Geometric Topology

Scientific paper

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102 pages, 13 figures. Slight revision of the statement of the main theorem, and a more complete discussion of the exterior of

Scientific paper

We give the first part of a proof of Thurston's Ending Lamination conjecture.
In this part we show how to construct from the end invariants of a Kleinian
surface group a ``Lipschitz model'' for the thick part of the corresponding
hyperbolic manifold. This enables us to describe the topological structure of
the thick part, and to give a-priori geometric bounds.

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