A Factorization of the Conway Polynomial

Abstract

A string link S can be closed in a canonical way to produce an ordinary closed link L. We also consider a twisted closing which produces a knot K. We give a formula for the Conway polynomial of L as a product of the Conway polynomial of K times a power series whose coefficients are given as explicit functions of the Milnor invariants of S. One consequence is a formula for the first non-vanishing coefficient of the Conway polynomial of L in terms of the Milnor invariants of L. There is an analogous factorization of the multivariable Alexander polynomial.