On Kontsevich integral of torus knots

Details On Kontsevich integral of torus knots On Kontsevich integral of torus knots

2003-10-08

arxiv.org/abs/math/0310111v3

Mathematics

Geometric Topology

10 pages, 4 figures

Scientific paper

We study the unwheeled rational Kontsevich integral of torus knots. We give a
precise formula for these invariants up to loop degree 3 and show that they
appear as colorings of simple diagrams. We show that they behave under cyclic
branched coverings in a very simple way. Our proof is combinatorial: it uses
the results of Wheels and Wheelings and new decorations of diagrams.

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