The universal Vassiliev-Kontsevich invariant for framed oriented links

Abstract

We give a generalization of the Reshetikhin-Turaev functor for tangles to get a combinatorial formula for the universal Vassiliev-Kontsevich invariant of framed oriented links which is coincident with the Kontsevich integral. The universal Vassiliev-Kontsevich invariant is constructed using the Drinfeld associator. We prove the uniqueness of the Drinfeld associator. As a corollary one gets the rationality of the Kontsevich integral. Many properties of the universal Vassiliev-Kontsevich invariant are established. Connections to quantum group invariants and to multiple zeta values are discussed.

24 pages

References in corpus (2)

• Link Invariants of Finite Type and Perturbation Theory
• Combinatorial expression for universal Vassiliev link invariant

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