Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

Details Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

1996-01-12

arxiv.org/abs/q-alg/9601009v1

Mathematics

Quantum Algebra

21 pages, 1 figure, LaTeX

Scientific paper

10.1007/BF02506408

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.

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