The Kontsevich integral and algebraic structures on the space of diagrams

Details The Kontsevich integral and algebraic structures on the space of diagrams The Kontsevich integral and algebraic structures on the space of diagrams

1999-09-24

arxiv.org/abs/math/9909151v3

Mathematics

Geometric Topology

17 pages, many figures, to appear in the proceedings of Knots in Hellas 1998, cross-listed to Quantum Algebra. Feb 22nd 2000:

Scientific paper

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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