We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus ...We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and 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.展开更多
A technique to compute the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then the author proves the volume conjecture for Whitehead doubles of a family of t...A technique to compute the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then the author proves the volume conjecture for Whitehead doubles of a family of torus knots and shows some interesting observations.展开更多
By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three...By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.展开更多
An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that t...An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.展开更多
基金Supported by the National Science Foundation of China（11471151） Supported by Program for Liaoning Excellent Talents in University（LR2011031）
Acknowledgment The authors would like to thank the referees for kind suggestions and many useful comments
文摘We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and 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.
文摘A technique to compute the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then the author proves the volume conjecture for Whitehead doubles of a family of torus knots and shows some interesting observations.
文摘By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
文摘By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.
文摘An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.
