Algebraic and Geometric Topology 2 (2002), paper no. 40, pages 1001-1050.

The Configuration space integral for links in R^3

Sylvain Poirier

Abstract. The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini, Martellini and Mintchev, Bar-Natan, Kontsevich, Bott and Taubes, D. Thurston, Altschuler and Freidel, Yang and others. We give a self-contained version of this study with a new choice of compactification, and we formulate a rationality result.

Keywords. Feynman diagrams, Vassiliev invariants, configuration space, compactification

AMS subject classification. Primary: 57M25. Secondary: 57J28.

DOI: 10.2140/agt.2002.2.1001

E-print: arXiv:math.GT/0005085

Submitted: 30 November 2001. (Revised: 15 July 2002.) Accepted: 21 July 2002. Published: 5 November 2002.

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Sylvain Poirier
3 bis rue Auguste Dollfus, 76600 Le Havre, France
Email: spoirier @laut re.net

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