On Universal Vassiliev Invariants

TL;DR

This paper proves the equivalence of the analytic and combinatorial definitions of universal Vassiliev invariants of links using properties of ordered exponentials and the Drinfeld associator.

Contribution

It establishes a rigorous connection between two different approaches to defining universal Vassiliev invariants, enhancing theoretical understanding.

Findings

Analytic and combinatorial definitions are equivalent

Uses properties of ordered exponentials and Drinfeld associator

Provides a foundation for further research in link invariants

Abstract

Using properties of ordered exponentials and the definition of the Drinfeld associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we prove that the analytic and the combinatorial definitions of the universal Vassiliev invariants of links are equivalent.