The Properties Of Polynomial Invariant Of Knots

This paper mainly talks about the differential properties of severalpolynomial invariants of a sort of link L. This especial kind of the link iscomposed of n knots in term of the hopf link. First,we make the kthderivative of the Jones polynomial V(L;t)of link L and some otherpolynomial invariants X(L;t),Φ(L;t) of link L which base on theJones polynomial, and research the divisibility of them when t=1, that isthe divisibility ofΦ_k(L)andφ_k(L). We disjoin linkLinto knots throughskein relation, then based on the properties of polynomial invariant of knot,sequentially we get the properties of polynomial invariant of link L. At thelast of the paper, we give an application about how to use the properties ofpolynomial invariant to class the knots.