Topology Seminar for 4/8/2003

Paul Melvin
Bryn Mawr College and the Institute for Advanced Study

The Milnor degree and quantum orders of 3-manifolds

The general purpose of this talk is to indicate how to use quantum invariants to address questions in classical low-dimensional topology.  In particular, we will show that the quantum orders of 3-manifolds (a measure of divisibility properties of quantum invariants with values in cyclotomic rings of integers) restrict the class of links in the 3-sphere that can arise in constructing a given 3-manifold by surgery.  This is joint work with Tim Cochran.