A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial

DOI10.1016/S0166-8641(02)00053-6zbMath1022.57007arXivmath/0106097OpenAlexW2070537242WikidataQ123128009 ScholiaQ123128009MaRDI QIDQ1868885

Lev Rozansky

Publication date: 28 April 2003

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0106097

zbMATH Keywords

Alexander polynomialKontsevich integralcolored Jones polynomialJacobi diagramMelvin-Morton-Rozansky conjecturerationality conjecture

Mathematics Subject Classification ID

Related Items

On Kontsevich integral of torus knots, A rational noncommutative invariant of boundary links, A non-commutative formula for the colored Jones function, A non-commutative Reidemeister-Turaev torsion of homology cylinders, The 3-loop polynomial of knots obtained by plumbing the doubles of two knots, On the 2-loop polynomial of knots, Whitehead doubling persists, A computation of the Kontsevich integral of torus knots, Topological formula of the loop expansion of the colored Jones polynomials, Cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial

Cites Work

• On a universal perturbative invariant of 3-manifolds
• The universal \(R\)-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial
• The Kontsevich integral and Milnor's invariants
• Wheels, wheeling, and the Kontsevich integral of the unknot
• The Århus integral of rational homology 3-spheres. II: Invariance and universality
• A rational noncommutative invariant of boundary links
• On the Melvin-Morton-Rozansky conjecture
• The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres