Current Developments in Mathematics

End Invariants and the Classification of Hyperbolic 3-Manifolds

Yair N. Minsky

Full-text: Open access


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".

Chapter information

D. Jerison, B. Mazur, T. Mrowka, W. Schmid, R. Stanley, S-T. Yau, eds. Current Developments in Mathematics, 2002 (Boston: International Press, 2003), 111-141

First available in Project Euclid: 29 June 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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.

Export citation