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arXiv:math/0502428 [math.GT]AbstractReferencesReviewsResources

The colored Jones polynomials and the Alexander polynomial of the figure-eight knot

Hitoshi Murakami

Published 2005-02-20Version 1

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.

Comments: 13 pages
Journal: JP J. Geom. Topol. 2 (2007), 249--269
Categories: math.GT
Subjects: 57M27, 57M25
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