On the Head and the Tail of the Colored Jones Polynomial

Details On the Head and the Tail of the Colored Jones Polynomial On the Head and the Tail of the Colored Jones Polynomial

2006-04-10

arxiv.org/abs/math/0604230v1

Compositio Math., Vol 142 (2006), No. 5, pp 1332-1342

Mathematics

Geometric Topology

14 pages, 6 figures

Scientific paper

The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.

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