The loop expansion of the Kontsevich integral, the null move and S-equivalence
Abstract
This is a substantially revised version. The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots. We introduce a second grading of the Kontsevich integral, the Euler degree, and a geometric null-move on the set of knots. We explain the relation of the null-move to S-equivalence, and the relation to the Euler grading of the Kontsevich integral. The null move leads in a natural way to the introduction of trivalent graphs with beads, and to a conjecture on a rational version of the Kontsevich integral, formulated by the second author and proven in joint work of the first author and A. Kricker.
Keywords
Cite
@article{arxiv.math/0003187,
title = {The loop expansion of the Kontsevich integral, the null move and S-equivalence},
author = {Stavros Garoufalidis and Lev Rozansky},
journal= {arXiv preprint arXiv:math/0003187},
year = {2007}
}
Comments
AMS-LaTeX, 20 pages with 31 figures