A Factorization of the Conway Polynomial

It is tempting to conjecture that there is some interesting relationship between the Conway polynomial ∇L(z) of a link L and ∇K(z), where K is a knot obtained by banding together the components of L. Obviously they cannot be equal since only terms of even or odd degree appear in ∇L(z), according to whether L has an odd or even number of components. Moreover there are many ways of choosing bands and one can easily see that the variety of knots one obtains can have very different polynomials. Nevertheless we will demonstrate that ∇L(z) and ∇K(z) have a very precise relationship in the form of a factorization: ∇L(z) = ∇K(z)Γ(z)