The Kontsevich integral and algebraic structures on the space of diagrams

Simon Willerton

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arXiv · math/9909151

The Kontsevich integral and algebraic structures on the space of diagrams

Simon Willerton

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Abstract

This paper is part expository and part presentation of calculational results. The target space of the Kontsevich integral for knots is a space of diagrams; this space has various algebraic structures which are described here. These are utilized with Le's theorem on the behaviour of the Kontsevich integral under cabling and with the Melvin-Morton Theorem, to obtain, in the Kontsevich integral for torus knots, both an explicit expression up to degree five and the general coefficients of the wheel diagrams.

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BibTeX RIS

Simon Willerton. 2000-02-22. The Kontsevich integral and algebraic structures on the space of diagrams. https://arxiv.org/abs/math/9909151

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