The colored Jones polynomials and the Alexander polynomial of the figure-eight knot
arXiv:math/0502428
Abstract
The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a three-manifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight knot the series converges in some cases and the limit equals the inverse of its Alexander polynomial.
arXiv comment13 pages
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