Foliations and pseudo-Anosov packages

In the late 70's, Thurston revolutionized 3-manifold topology by proving his famous Geometrization Theorem for Haken manifolds. A 3-manifold is Haken if it is irreducible (every embedded sphere bounds a ball) and if it contains an embedded, 2-sided incompressible surface (one whose fundamental group injects into that of the 3-manifold). The hardest case of Thurston's proof is the case in which the topology of the manifold is simplest: M is a surface bundle over a circle. In the last few years, a conjectural picture of the theory of taut foliations has emerged which resembles in many ways the picture for a surface bundle over a circle. We will describe this conjectural picture, point out the analogy with the fibered case, and indicate what is known and what is still unknown.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).