Abstract:

We give a formula for the coefficient of the z^2-term of the Alexander-Conway polynomial of any oriented knot K in terms of the sum of determinants of the blocks of 2 × 2 sub-matrices of the Seifert matrix of K, where each determinant represents a self-linking in an explicit way, and therefore the coefficient gives a measure of self-linking of K in that sense. The method used in this paper can be generalized to give a formula for the general coefficients of the Alexander-Conway polynomial for any oriented link L, and the results are forthcoming.