Cabling the Vassiliev Invariants

Details Cabling the Vassiliev Invariants Cabling the Vassiliev Invariants

1995-11-27

arxiv.org/abs/q-alg/9511024v4

Mathematics

Quantum Algebra

LaTeX2e, 31 pages. This version to appear in the Journal of Knot Theory and it's Ramifications

Scientific paper

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.

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