Volume 2, issue 2 (2002)

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The configuration space integral for links in $\mathbb R^3$

Sylvain Poirier

Algebraic & Geometric Topology 2 (2002) 1001–1050
 arXiv: math.GT/0005085
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
Primary: 57M25
Secondary: 57J28