Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 12, pages 183--199.

On configuration space integrals for links

Christine Lescop

Abstract. We give an introductory survey on the universal Vassiliev invariant called the perturbative series expansion of the Chern-Simons theory of links in euclidean space, and on its relation with the Kontsevich integral. We also prove an original geometric property of the anomaly of Bott, Taubes, Altschuler, Freidel and D. Thurston, that allowed Poirier to prove that the Chern-Simons series and the Kontsevich integral coincide up to degree 6.

Keywords. Kontsevich Integral, Chern-Simons theory, Vassiliev invariants, links, knots, tangles, configuration spaces, quantum invariants, Jacobi diagrams

AMS subject classification. Primary: 57M27. Secondary: 57M25, 17B37, 81T18.

E-print: arXiv:math.GT/0211062

Submitted to GT on 19 December 2001. (Revised 15 February 2002.) Paper accepted 22 July 2002. Paper published 21 September 2002.

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Christine Lescop
CNRS, Institut Fourier, B.P.74, 38402 Saint-Martin-d'Heres cedex, France
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