The Conway Polynomial Of 4-tangles

Alexander polynomial is the first polynomial invariant of the knots,then Conway normalizes Alexander polynomial into Conway polynomial and introduces Conway notation.This polynomial can be computed by using skein relations from intersection points of the regular projection graph.In this paper,the orientation of 4-tangles is defined on the basis of previous researches,and some theorems are obtained on the basis of this orientation.Applying these theorems we can calculate Conway polynomials of the the concatenation of two such basic 4-tangles and Conway polynomials of the the concatenation of two such 4-tangles.Furthermore,only the polynomials of two basic 4-tangles need to be calculated by drawing,the others can be obtained by algebraic operation of known polynomials.So,this method simplifies the process of calculating the Conway polynomial of 4-tangles.