On ordered sequences for link diagrams with respect to Reidemeister moves I and III

Kishin Sasaki

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arXiv · 2205.06490

On ordered sequences for link diagrams with respect to Reidemeister moves I and III

Kishin Sasaki

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Abstract

We first prove that, infinitely many pairs of trivial knot diagrams that are transformed into each other by applying Reidemeister moves I and III are NOT transformed into each other by a sequence of the Reidemeister moves I that increase the number of crossings, followed by a sequence of Reidemeister moves III, followed by a sequence of the Reidemeister moves I that decrease the number of crossings. To create a simple sequence between link diagrams that are transformed into each other by applying finitely many Reidemeister moves I and III, we prove that the link diagrams are always transformed into each other by applying an I-generalized ordered sequence.

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Kishin Sasaki. 2022-05-13. On ordered sequences for link diagrams with respect to Reidemeister moves I and III. https://arxiv.org/abs/2205.06490

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