Zeros of Jones polynomials for families of knots and links

S. C. Chang; R. Shrock

doi:10.1016/S0378-4371(01)00364-8

Zeros of Jones polynomials for families of knots and links

S. C. Chang
, R. Shrock

Institute for Theoretical Physics

Stony Brook University

Stony Brook University

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	196-218
Number of pages	23
Journal	Physica A: Statistical Mechanics and its Applications
Volume	301
Issue number	1-4
DOIs	https://doi.org/10.1016/S0378-4371(01)00364-8
State	Published - Dec 1 2001

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title = "Zeros of Jones polynomials for families of knots and links",

abstract = "We calculate Jones polynomials VL(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 VL(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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T1 - Zeros of Jones polynomials for families of knots and links

AU - Chang, S. C.

AU - Shrock, R.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - We calculate Jones polynomials VL(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 VL(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.

AB - We calculate Jones polynomials VL(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 VL(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.

UR - https://www.scopus.com/pages/publications/0035575821

U2 - 10.1016/S0378-4371(01)00364-8

DO - 10.1016/S0378-4371(01)00364-8

M3 - Article

SN - 0378-4371

VL - 301

SP - 196

EP - 218

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-4

ER -

Zeros of Jones polynomials for families of knots and links

Abstract

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