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Distance between links by zero-linking twists. (English) Zbl 0896.57005

A zero-linking twist applied to a link \(L_0\subset S^3\) is a move which does \(1/n\) surgery along an unknotted circle \(k\) disjoint from \(L_0\), thus transforming \(L_0\) into a link \(L_1\) of the same multiplicity. A special case is the change of a crossing. So, any two links of the same multiplicity can be transformed into each other by zero-linking-twists, and the minimal number of twists needed defines a distance \(d^\tau (L_0,L_1)\). The author gives a lower bound of \(d^\tau (L_0,L_1)\) in terms of ranks of Alexander-type modules and local signature invariants. Examples are presented. As an application it is shown that there are knots with arbitrarily large \(d^\tau\)-distances to the class of fibred knots.

MSC:

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