Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial
- 67 Downloads
We formulate a conjecture about the structure of “upper lines” in the expansion of the colored Jones polynomial of a knot in powers of (q−1). The Melvin-Morton conjecture states that the bottom line in this expansion is equal to the inverse Alexander polynomial of the knot. We conjecture that the upper lines are rational functions whose denominators are powers of the Alexander polynomial. We prove this conjecture for torus knots and give experimental evidence that it is also true for other types of knots.
KeywordsHigh Order Term Jones Polynomial Alexander Polynomial Rational Homology Sphere Skein Relation
Unable to display preview. Download preview PDF.
- 1.Alvarez, M., Labastida, J.M.F.: Vassiliev Invariants for Torus Knots. Preprint q-alg/9506009Google Scholar
- 3.Bar-Natan, D., Garoufalidis, S.: On the Melvin-Morton-Rozansky Conjecture. Preprint, 1994Google Scholar
- 8.Kauffman, L., Lins, S.: Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds.Google Scholar
- 13.Rozansky, L. Residue Formulas for the Largek Asymptotics of Witten's Invariants of Seifert Manifolds. The Case ofSU(2). Preprint UMTG-179, hep-th/9412075Google Scholar
- 14.Rozansky, L.: Witten's Invariants of Rational Homology Spheres at Prime Values ofK and Trivial Connection Contribution. Preprint UMTG-183, q-alg/9504015, to appear in Commun. Math. Phys.Google Scholar
- 15.Rozansky, L.: On Finite Type Invariants of Links and Rational Homology Spheres Derived from the Jones Polynomial and Witten-Reshetikhin-Turaev Invariant. Preprint q-alg/9511025Google Scholar
- 16.Rozansky, L.: Onp-adic Convergence of Perturbative Invariants of some Rational Homology Spheres. Preprint q-alg/9601015Google Scholar
- 17.Rozansky, L.: The UniversalR-Matrix, Burau Representation and the Melvin-Morton Expansion of the Colored Jones Polynomial. Preprint q-alg/9604005Google Scholar