Current Developments in Mathematics
End Invariants and the Classification of Hyperbolic 3-Manifolds
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".
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, 111--141, International Press of Boston, Boston, MA, 2003. https://projecteuclid.org/euclid.cdm/1088530401