MSCS Graduate Student Seminar
Fall 2000
October 27 and November 3
SPEAKER: Peter Shalen
TITLE: Topology in three dimensions I & II
ABSTRACT: The traditional objects of study in differential geometry are curves,
surfaces, and their generalizations to arbitrary dimenions, known as
manifolds. It has been recognized since the time of Gauss that the
topological invariants of a manifold impose restrictions on its
geometry. This is one of the reasons why the study of the topology of
manifolds has attracted the attention of so many mathematicians for
the last 100 years. While progress on the topological theory of
manifolds in all dimensions has been remarkable, the theory turns out
to be especially rich in dimension 3 because of its uniquely close
interaction with the geometric theory. I will try to communicate
something of the flavor of the subject.