The loop expansion of the Kontsevich integral, the null move and S-equivalence

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
AMS-LaTeX, 20 pages with 31 figures

Keywords

Geometric Topology, Quantum Algebra

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/58919

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0003187
 http://arxiv.org/abs/math/0003187

Collections

arXiv