Algebraic and Geometric Topology 2 (2002),
paper no. 40, pages 1001-1050.
The Configuration space integral for links in R^3
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.
Feynman diagrams, Vassiliev invariants, configuration space, compactification
AMS subject classification.
Submitted: 30 November 2001.
(Revised: 15 July 2002.)
Accepted: 21 July 2002.
Published: 5 November 2002.
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