Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial
arXiv:q-alg/9601009 · doi:10.1007/BF02506408
Abstract
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.
21 pages, 1 figure, LaTeX
References in corpus (3)
Cited by in corpus (21)
- Analytic Continuation Of Chern-Simons Theory
- Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
- The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
- A volume-ish theorem for the Jones polynomial of alternating knots
- A rational noncommutative invariant of boundary links
- Quantum Knot Invariant for Torus Link and Modular Forms
- Does the Jones polynomial determine the signature of a knot?
- Cabled Wilson Loops in BF Theories
- Resurgent Analysis for Some 3-manifold Invariants
- BPS Invariants for a Knot in Seifert Manifolds
- Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
- Knot Complement, ADO-Invariants and their Deformations for Torus Knots
- A computation of the Kontsevich integral of torus knots
- A Cable Knot and BPS-Series
- A cabling formula for the 2-loop polynomial of knots
- On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres
- On p-Adic Convergence of Perturbative Invariants of Some Rational Homology Spheres
- A Cable Knot and BPS-Series II
- On Bar-Natan - van der Veen's perturbed Gaussians
- On Habiro's cyclotomic expansions of the Ohtsuki invariant
- On Kontsevich integral of torus knots