The Kontsevich integral and algebraic structures on the space of diagrams
Abstract
Description
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.
17 pages, many figures, to appear in the proceedings of Knots in Hellas 1998, cross-listed to Quantum Algebra. Feb 22nd 2000: sign error in definition of STU relation corrected
17 pages, many figures, to appear in the proceedings of Knots in Hellas 1998, cross-listed to Quantum Algebra. Feb 22nd 2000: sign error in definition of STU relation corrected