Unknotting number and number of Reidemeister moves needed for unlinking

Details Unknotting number and number of Reidemeister moves needed for unlinking Unknotting number and number of Reidemeister moves needed for unlinking

2010-12-18

arxiv.org/abs/1012.4131v2

Mathematics

Geometric Topology

10pages, 8 figures

Scientific paper

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.

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