A factorization of the Conway polynomial

Abstract

It is shown that the Conway polynomial of a link is a product of two factors, the first of which is the Conway polynomial of a knot obtained by banding together the link components and the second is determined, via an explicit formula, by the $\tilde{\mu }$-invariants of the link. In particular we get a formula, in terms of the 7-invariants, for the first non-zero coefficient of the Conway polynomial. A similar formula is obtained for the multi-variable Alexander-polynomial.