11/11/2004

David Gabai
Princeton University

Shrinkwrapping and the Taming of Hyperbolic 3-Manifolds

We show that if N is a complete hyperbolic 3-manifold with finitely generated fundamental group, then N is the interior of a compact 3-manifold; thereby obtaining a positive proof of the "Marden Conjecture" also known as the "Tameness Conjecture" (Also proven by Ian Agol).  A key ingredient is Shrinkwrapping which is a method for producing surfaces of intrinsic curvature ¾-1.    We will discuss some of its many applications to hyperbolic geometry and 3-manifold topology.  (This is joint work with Danny Calegari).