Mathematics Department Colloquium
Spring 2005

Date: Thursday, February 3
Time: 4:00 p.m.
Location: 215 Thomas Building
Name: David Gabai
Affiliation: Princeton University
Title: Shrinkwrapping and the Taming of Hyperbolic 3-Manifolds

Abstract: In 1935 J. H. C. Whitehead found an example of a contractible open 3-manifold which is not $ \mathbb{R}^3$. Similar constructions lead to wild manifolds with fundamental group the free group on n generators. The recently proved Tameness (Marden) Conjecture shows that hyperbolic 3-manifolds are topologically tame.

Theorem. (Agol, Calegari-Gabai) If $ N$ is a complete hyperbolic 3-manifold with finitely generated fundamental group, then $ N$ is diffeomorphic to the interior of a compact 3-manifold.

We will discuss ideas behind the proof of this result as well as some applications.