摘要: §l. INTRODUCTION THE CLASSICAL Alexander polynomial[l] A(x) = A&) of a knot or link K C S3 is an invariant ambient isotopy that well-defined up to sign and multiplication by powers the variable x. The Conway polynomial V(z) V,(z) direct isotopy. This polynomial, first introduced in[2], has remarkable properties allow its computation from diagram without recourse matrices determinants. It related via potential function V(x x-‘) which (up x) equivalent A(x*). purpose this paper give exposition explain source modelling it in analogy polynomial. There good geometric explanation for function: proceeds as follows: Given oriented S3, let F be connected, spanning surface K. Let 8: H,(F) x H,(F)+2 Seifert pairing (see 03). 0 also denote any matrix with respect basis H,(F). Define potenfiaI a,(x) formula 0,(x) 0(x0 -x-‘(Y) where D denotes determinant 8’ transpose 8. (If 0, n,(x) 1). Our main result following:
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