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Perturbative 3-manifold invariants by cut-and-paste topology
Geometry/Topology| Speaker: | Greg Kuperberg, Mathematics, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Nov 3 1999, 4:10PM |
About five years ago Kontsevich and others interpreted Vassiliev invariants of knots and links in terms of perturbative Chern-Simons field theory. The invariants, expressed in terms of integrals, constitute a sweeping generalization of the Gauss formula for the linking number of two knots in R3. In the more general setting of 3-manifold invariants, there was a gap between the theory of finite-type invariants (generalizing Vassiliev) and invariants defined by integrals (arising from Chern-Simons). Recently Dylan Thurston and I bridged this gap, first by clarifying the integral invariants as purely topological, and second by showing that they are finite type as predicted.