On Kontsevich integral of torus knots

Julien Marche

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On Kontsevich integral of torus knots

Julien Marche

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Abstract

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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BibTeX RIS

Julien Marche. 2003-12-09. On Kontsevich integral of torus knots. https://arxiv.org/abs/math/0310111

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