Configuration space integrals and invariants for 3-manifolds and knots

Cattaneo, A S (1999). Configuration space integrals and invariants for 3-manifolds and knots. In: Nencka, H. Low-dimensional topology (Funchal, 1998). Providence, RI: American Mathematical Society, 153-165.

Abstract

The first part of this paper is a short review of the construction of invariants of rational homology 3-spheres and knots in terms of configuration space integrals.
The second part describes the relationship between the above construction and Kontsevich's proposal of removing one point from the rational homology sphere. Explicit formulae are computed. In the case of the "Theta" invariant, a comparison with Taubes's construction is briefly discussed.

Abstract

The first part of this paper is a short review of the construction of invariants of rational homology 3-spheres and knots in terms of configuration space integrals.
The second part describes the relationship between the above construction and Kontsevich's proposal of removing one point from the rational homology sphere. Explicit formulae are computed. In the case of the "Theta" invariant, a comparison with Taubes's construction is briefly discussed.