Mathematics Colloquium
3:00 p.m.
Math Annex 1100
Danny Calegari
California Institute of Technology
Foliations and pseudoAnosov packages
In the late 70's, Thurston revolutionized 3manifold topology
by proving his famous Geometrization Theorem for Haken manifolds.
A 3manifold is Haken if it is irreducible (every embedded sphere
bounds a ball) and if it contains an embedded, 2sided incompressible
surface (one whose fundamental group injects into that of the
3manifold). 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).
