Cabling the Vassiliev Invariants
q-alg
2008-02-03 v4 Quantum Algebra
Abstract
We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described over the cable eigenbasis. The action of immanent weight systems on general Feynman diagrams is considered, and the highest eigenvalue cabling eigenvectors are shown to be dual to the immanent weight systems. Using these results, we prove a recent conjecture of Bar-Natan and Garoufalidis on cablings of weight systems.
Keywords
Cite
@article{arxiv.q-alg/9511024,
title = {Cabling the Vassiliev Invariants},
author = {A. Kricker and B. Spence and I. Aitchison},
journal= {arXiv preprint arXiv:q-alg/9511024},
year = {2008}
}
Comments
LaTeX2e, 31 pages. This version to appear in the Journal of Knot Theory and it's Ramifications