Algebraic and Geometric Topology 4 (2004), paper no. 51, pages 1155-1175.

A computation of the Kontsevich integral of torus knots

Julien Marche

Abstract. We study the rational Kontsevich integral of torus knots. We construct explicitely a series of diagrams made of circles joined together in a tree-like fashion and colored by some special rational functions. We show that this series codes exactly the unwheeled rational Kontsevich integral of torus knots, and that it behaves very simply under branched coverings. Our proof is combinatorial. It uses the results of Wheels and Wheeling and various spaces of diagrams.

Keywords. Finite type invariants, Kontsevich integral, torus knots, Wheels and Wheeling, rationality

AMS subject classification. Primary: 57M27. Secondary: 57M25, 57R56.

DOI: 10.2140/agt.2004.4.1155

E-print: arXiv:math.GT/0404264

Submitted: 6 May 2004. (Revised: 8 November 2004.) Accepted: 15 November 2004. Published: 10 December 2004.

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Julien Marche
Institut de Mathematiques de Jussieu, Equipe `Topologie et Geometries Algebriques'
Case 7012, Universite Paris VII, 75251 Paris CEDEX 05, France

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