A computation of the Kontsevich integral of torus knots

Details A computation of the Kontsevich integral of torus knots A computation of the Kontsevich integral of torus knots

2004-04-14

arxiv.org/abs/math/0404264v2

Algebr. Geom. Topol. 4 (2004) 1155-1175

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-51.abs.html

Scientific paper

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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