The universal Vassiliev-Kontsevich invariant for framed oriented links

TL;DR

This paper generalizes the Reshetikhin-Turaev functor to provide a combinatorial formula for the universal Vassiliev-Kontsevich invariant of framed oriented links, linking quantum invariants and multiple zeta values.

Contribution

It introduces a new combinatorial formula for the universal Vassiliev-Kontsevich invariant using the Drinfeld associator, establishing its uniqueness and rationality.

Findings

Provides a combinatorial formula coincident with the Kontsevich integral

Proves the uniqueness of the Drinfeld associator

Discusses connections to quantum groups and multiple zeta values

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.