HOMFLY polynomials for 3-component links with v-span 4

Abstract

The HOMFLY polynomial PL(v,z) of a link L is a well known link invariant with two variables v and z, which generalizes the Jones polynomial. The v-span of the HOMFLY polynomial is the difference between the maximum and the minimum degrees of the polynomial in the variable v. We show the HOMFLY polynomial of the 3-component link with v-span 4 is determined by the Jones polynomial.