Parallel version of the universal Vassiliev-Kontsevich invariant Original Research Article

Let image be the universal Vassiliev-Kontsevich invariant for framed links in [13], which is a generalization of Kontsevichʹs invariant in [10, 1], Let K be a framed knot and K(r) be its r parallel. Then we show image, where Δ(r) is an operation of chord diagrams which replace the Wilson loop by r copies. We calculate the values of image of the Hopf links and the change of image under the Kirby moves. An explicit formula of an important normalization factor, which is the value of the trivial knot, in the universal enveloping algebra U(g) of any Lie algebra is given.