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Concordance invariance of coefficients of Conway’s link polynomial. (English) Zbl 0589.57005
The Conway polynomial of a link in \(S^ 3\) is an invariant of the isotopy class of the link, and is related to the classical Alexander polynomial by a change of variable and a normalization. An important problem is to determine which data of this polynomial are cobordism invariants, i.e. are invariant under concordance of links. The author shows that the first non-vanishing coefficient, as well as the mod 2 reduction of the next coefficient, of this polynomial are invariant under link concordance. For 2- and 3-component links, he also gives a geometric interpretation of this first non-vanishing coefficient. He also obtains similar results for the mod 2 reduction of the Conway polynomial and for the 2-variable polynomial introduced by P. Freyd et al. [Bull. Am. Math. Soc. 12, 239-246 (1985; Zbl 0572.57002)].
Reviewer: F.Bonahon

MSC:
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:
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