A volume-ish theorem for the Jones polynomial of alternating knots

Details A volume-ish theorem for the Jones polynomial of alternating knots A volume-ish theorem for the Jones polynomial of alternating knots

2004-03-25

arxiv.org/abs/math/0403448v1

Pacific J. Math. 231 (2007), no. 2, 279--291

Mathematics

Geometric Topology

14 pages

Scientific paper

10.2140/pjm.2007.231.279

The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coefficients of the Jones polynomial is bounded from above and from below by constants. Furthermore, we give experimental data on the relation of the growths of the hyperbolic volume and the coefficients of the Jones polynomial, both for alternating and non-alternating knots.

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