Canonical splittings of groups and 3-manifolds
by
Peter Scott
University of Michigan
Coauthors: Gadde Swarup (University of Melbourne)

In the mid 1970's, Jaco and Shalen, and independently Johannson, proved that Haken 3-manifolds have a canonical submanifold (possibly empty) called the characteristic submanifold, and they showed that this submanifold has some important properties. Starting in the mid 1980's, there has been a whole series of algebraic results which describe analogous results in group theory. However, none of these results yields as much information as the topological result when applied to the fundamental group of a Haken 3-manifold.

In this talk, I will discuss recent joint work with Gadde Swarup of the University of Melbourne in which we give a new approach to this area. We obtain new algebraic results which yield the topological result when applied to the fundamental group of a Haken 3-manifold.

Date received: February 6, 2001