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 . 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 is a complete hyperbolic 3-manifold with finitely generated fundamental group, then 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.