About the uniqueness and the denominators of the Kontsevich Integral

Details About the uniqueness and the denominators of the Kontsevich Integral About the uniqueness and the denominators of the Kontsevich Integral

2000-04-14

arxiv.org/abs/math/0004094v1

Journal of Knot Theory and Its Ramifications, Vol. 11, 5 (2002) 759-780

Mathematics

Geometric Topology

LaTeX, 23 pages, uses pstricks

Scientific paper

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 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 the space of Feynman diagrams which transforms the Kontsevich Integral into the Poirier limit of the perturbative expression of the Chern-Simons theory, as a function of the anomaly. We use this corollary to improve the Le estimates on the denominators of the Kontsevich Integral.

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