On the Head and the Tail of the Colored Jones Polynomial

Oliver T. Dasbach; Xiao-Song Lin

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On the Head and the Tail of the Colored Jones Polynomial

Oliver T. Dasbach·Xiao-Song Lin

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Abstract

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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BibTeX RIS

Oliver T. Dasbach, Xiao-Song Lin. 2006-04-10. On the Head and the Tail of the Colored Jones Polynomial. https://arxiv.org/abs/math/0604230

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