Zeros of Jones Polynomials for Families of Knots and Links
Shu-Chiuan Chang, Robert Shrock (Yang Inst. for Theoretical, Physics, State Univ. of New York at Stony Brook)
TL;DR
This paper computes Jones polynomials for various families of alternating knots and links using Tutte polynomials, analyzes their zeros, and discusses extensions to non-alternating links.
Contribution
It introduces a method to calculate Jones polynomials via Tutte polynomials and analyzes the zeros for infinite families of knots and links.
Findings
Zeros of Jones polynomials form specific accumulation sets
Method links Jones polynomials to Tutte polynomials for alternating links
Includes discussion on non-alternating links
Abstract
We calculate Jones polynomials for several families of alternating knots and links by computing the Tutte polynomials for the associated graphs and then obtaining 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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