环面结和二桥结Jones多项式的零点

韩友发, 张容玮, 王琳琳, 马晓莎

doi:10.13371/j.cnki.chin.q.j.m.2014.04.016

数学季刊 >

2014 , Vol. 29 >Issue 4: 612 - 619

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.016

环面结和二桥结Jones多项式的零点

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School of Mathematics, Liaoning Normal University

HAN You-fa(1962-), male, native of Changchun, Jilin, a professor of Liaoning Normal University, Ph.D., engages in low-dimension topology.

收稿日期: 2013-08-25

网络出版日期: 2020-11-27

基金资助

Supported by the National Science Foundation of China(11471151)； Supported by Program for Liaoning Excellent Talents in University(LR2011031)；

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Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots

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School of Mathematics, Liaoning Normal University

HAN You-fa(1962-), male, native of Changchun, Jilin, a professor of Liaoning Normal University, Ph.D., engages in low-dimension topology.

Received date: 2013-08-25

Online published: 2020-11-27

Supported by

Supported by the National Science Foundation of China(11471151)； Supported by Program for Liaoning Excellent Talents in University(LR2011031)；

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摘要

We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e^{（2m+1）πi/2}and e^{（2m+1）πi/4}（m is a positive integer）can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C（-2, 2, ···,（-1）^r2） by the recursive form and discuss the distribution of their zeros.

关键词： Jones polynomial; zeros; torus knot; 2-bridge knot

本文引用格式

韩友发, 张容玮, 王琳琳, 马晓莎 . 环面结和二桥结Jones多项式的零点[J]. 数学季刊, 2014 , 29(4) : 612 -619 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.016

Abstract

Key words： Jones polynomial; zeros; torus knot; 2-bridge knot

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