Jones Polynomials Of Some Links And Their Zeros

This thesis analyzes the Jones polynomials of some knots and links and their zeros.Based on one projection of some knots and links,this thesis uses the thought of splitting,a knot or link is divided into the composition of several knots and links.According to the relationship between the Jones polynomial and bracket polynomial,this thesis firstly uses the property of bracket polynomial to calculate itself and calculates the writhes,and then gets its Jones polynomial.Finally,through the method of factorization,the partial factor of Jones polynomial of two-torus knots is as the partial factor of the Jones polynomial of these knots and links.Using the properties of Jones polynomials of knots and links and the knowledge of the zeros distribution of Jones polynomial of two-torus knots,the problem of whether some unit roots are their zeros is considered.Firstly,this thesis introduces the basic concepts of knots,including the definition of knots and links,trivial knots and links and the definition of the writhes.And then this thesis gives the polynomials of knots,including bracket polynomial and Jones polynomial,and their relationship.Next,the definition of the torus knots and the zeros distribution of the two-torus knots are given.Finally,the definition of the links studied in this thesis is briefly explained.Then,this thesis studies the bracket polynomial and the Jones polynomial of some knots and links.By continuously applying the deformation formula...