About the uniqueness and the denominators of the Kontsevich

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About the uniqueness and the denominators of the Kontsevich integral Christine Lescop April 10, 2000 Abstract We rene a theorem of Le and Murakami about the uniqueness of framed link invariants derived from good monoidal functors from the category of framed q-tangles to the category of spaces of Feynman diagrams. As a corollary, we prove that the Altschuler and Freidel anomaly 2 A(S 1 ) -that groups the Bott and Taubes anomalous terms- is a combination of diagrams with two univalent vertices and we explicitly dene the isomorphism of A 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 . As a consequence of this corollary, we use the Poirier estimates on the denominators of the perturbative expression of the Chern-Simons theory to show that the denominators of the degree n part of the Kontsevich integral of framed links divide into (2!3! : : : (n5)!)(n5)!3 2 (3n4)!2 2n+2 for n 5. 1 Introduction There are essentially two universal Vassiliev invariants of links, the Kontsevich integral, and the perturbative expression of the Chern-Simons theory studied by Guadagnini Martellini and Mintchev, Bar-Natan, Kontsevich, Bott and Taubes [BT], D.

  • vassiliev invariant

  • framed link invariants

  • diagrams obtained

  • any framed link

  • topological vector spaces

  • kontsevich integral

  • represented without horizontal

  • relation when


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