Current Developments in Mathematics

End Invariants and the Classification of Hyperbolic 3-Manifolds

Yair N. Minsky

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These notes are a biased guide to some recent developments in the deformation theory of hyperbolic 3-manifolds and Kleinian groups. This field has its roots in the work of Poincaré and Klein, and connects to topology via Thurston's geometrization program, to analysis via the Ahlfors-Bers quasiconformal theory, and to complex dynamics via the work of Thurston, Sullivan and others. It encompasses many techniques and ideas and may be too big a subject for a single account. We will focus on the geometric study of ends of hyperbolic 3-manifolds and boundaries of deformation spaces, and in particular on the techniques that led to the recent solution by Brock, Canary and the author [82, 23] of the incompressible-boundary case of Thurston's "Ending Lamination Conjecture".

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Current Developments in Mathematics, Volume 2002 (2002), 111-141.

First available in Project Euclid: 29 June 2004

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Minsky, Yair N. End Invariants and the Classification of Hyperbolic 3-Manifolds. Current Developments in Mathematics 2002 (2002), 111--141.

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