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A computation of the Kontsevich integral of torus knots

Julien Marche

Published 2004-04-14, updated 2004-12-15Version 2

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.

Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-51.abs.html
Journal: Algebr. Geom. Topol. 4 (2004) 1155-1175
Categories: math.GT
Subjects: 57M27, 57M25, 57R56
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