Unknotting number and number of Reidemeister moves needed for unlinkingReport as inadecuate



 Unknotting number and number of Reidemeister moves needed for unlinking


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Using unknotting number, we introduce a link diagram invariant of Hass and Nowik type, which changes at most by 2 under a Reidemeister move. As an application, we show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being unknotted with respect to the number of crossings. Assuming a certain conjecture on unknotting numbers of a certain series of composites of torus knots, we show that the above diagrams need quadratic number of Reidemeister moves for being splitted.



Author: Chuichiro Hayashi; Miwa Hayashi

Source: https://archive.org/







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