A computation of the Kontsevich integral of torus knots

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.

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Keywords

finite type invariants, Kontsevich integral, torus knots, Wheels, Wheeling, rationality

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M25, 57R56

References

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Publication

Received: 6 May 2004

Revised: 8 November 2004

Accepted: 15 November 2004

Published: 10 December 2004

Authors

Julien Marche
Institut de Mathématiques de Jussieu Équipe “Topologie et Géométries Algébriques” Case 7012 Université Paris VII 75251 Paris Cedex 05 France

Volume 4, issue 2 (2004)

Julien Marche

Abstract