Math Annex 1100
California Institute of Technology
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).