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

Hitoshi Murakami

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arXiv · math/0502428

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

Hitoshi Murakami

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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.

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BibTeX RIS

Hitoshi Murakami. 2005-02-20. The colored Jones polynomials and the Alexander polynomial of the figure-eight knot. https://arxiv.org/abs/math/0502428

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