JP Journal of Geometry and Topology
Volume 7, Issue 2, Pages 249 - 269
(July 2007)
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THE COLORED JONES POLYNOMIALS AND THE ALEXANDER POLYNOMIAL OF
THE FIGURE-EIGHT KNOT
Hitoshi Murakami (Japan)
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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. |
| Keywords and phrases: figure-eight knot, colored Jones polynomial, Alexander polynomial, volume conjecture. |
| Communicated by Yasuo Matsushita |
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