Zeros of Jones Polynomials for Families of Knots and Links

Details Zeros of Jones Polynomials for Families of Knots and Links Zeros of Jones Polynomials for Families of Knots and Links

2001-03-29

arxiv.org/abs/math-ph/0103043v2

Physica A 301, 196-218 (2001)

Physics

Mathematical Physics

30 pages, latex, 9 postscript figures; minor rewording on a reference, no changes in results

Scientific paper

10.1016/S0378-4371(01)00364-8

We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial. For each of these families we determine the zeros of the Jones polynomial, including the accumulation set in the limit of infinitely many crossings. A discussion is also given of the calculation of Jones polynomials for non-alternating links.

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