Geodesic
A computation of the Kontsevich integral of torus knots
Marche, Julien1
1Institut de Mathématiques de Jussieu, Équipe “Topologie et Géométries Algébriques”, Case 7012, Université Paris VII, 75251 Paris Cedex 05, France
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1155-1175
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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.

DOI : 10.2140/agt.2004.4.1155
Keywords: finite type invariants, Kontsevich integral, torus knots, Wheels, Wheeling, rationality

Marche, Julien  1

1 Institut de Mathématiques de Jussieu, Équipe “Topologie et Géométries Algébriques”, Case 7012, Université Paris VII, 75251 Paris Cedex 05, France 
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Marche, Julien. A computation of the Kontsevich integral of torus knots. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1155-1175. doi: 10.2140/agt.2004.4.1155

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