ABOUT THE UNIQUENESS OF THE KONTSEVICH INTEGRAL

We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in order to specify the relationship between the two (possibly equal) main universal Vassiliev link invariants: the Kontsevich Integral and the perturbative expression of the Chern-Simons theory. As a corollary, we prove that the Altschuler and Freidel anomaly -that groups the Bott and Taubes anomalous terms- is a combination of diagrams with two univalent vertices and we explicitly define the isomorphism of which transforms the Kontsevich integral into the Poirier limit of the perturbative expression of the Chern-Simons theory for framed links, as a function of α