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The Jones polynomial of ribbon links. (English) Zbl 1178.57002

The author studies the Jones polynomial from a topological point of view, with an eye toward finding results analogous to those known for the Alexander polynomial. For ribbon links, a Jones nullity is defined which features similarities to Murasugi’s nullity defined from the Seifert form. A family of link invariants generalizing the determinant is obtained. These invariants turn out to be of finite type with respect to band crossing changes, though not with respect to crossing changes. Certain congruences are found to hold for the generalized determinants.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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