After a short presentation of the theory of Vassiliev knot invariants, we shall introduce a universal finite type invariant for knots in the ambient space. This invariant is often called the perturbative series expansion of the Chern-Simons theory of links in the Euclidean space. It will be constructed as a series of integrals over configuration spaces. We shall also review similar constructions in the theory of finite type invariants of 3-manifolds.
Introduction to the Vassiliev knot invariants with the example of the Jones polynomial and the presentation of Jacobi-Feynman diagrams.
Introduction to the configuration space integrals with the example of the Gauss definition of the linking number.
The "Kontsevich, Bott, Taubes, Bar-Natan, Altschuler, Freidel, D. Thurston" link invariant Z.
Some properties of Z including its universality among Vassiliev invariants.
Similar constructions in the theory of finite type invariants of 3-manifolds. Questions and problems.
Updated 04/03/2005