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Sharp Bounds on Some Classical Knot Invariants
Preview AbstractThere are obvious inequalities relating the Nakanishi index of a knot, the bridge number, the degree 2n of the Alexander polynomial and the length of the chain of Alexander ideals. We give examples for every positive value of n to show that these bounds are sharp.
NEW INVARIANTS OF SIMPLE KNOTS
Preview AbstractOur longterm plan is to classify knot modules and pairings by utilizing the power of computational number theory. The first step in this is to define invariants for which any given value arises from only finitely many modules: this is the purpose of the present paper.