Wheels, Wheeling, and the Kontsevich Integral of the Unknot

1997/03/13 by Dror Bar-Natan, Bar-Natan, Dror, Stavros Garoufalidis +5 · 2 citations
Mathematics · #Geometric and Algebraic Topology #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.q-alg/9703025

Abstract

We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products on the space of Chinese characters. The two formulas use the related notions of "Wheels" and "Wheeling". We prove these formulas "on the level of Lie algebras" using standard techniques from the theory of Vassiliev invariants and the theory of Lie algebras.

Cited by

• Goldman-Turaev formality from the Kontsevitch integral
• Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne

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