On ordered sequences for link diagrams with respect to Reidemeister moves I and III
Geometric Topology
2023-09-12 v2
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.
Cite
@article{arxiv.2205.06490,
title = {On ordered sequences for link diagrams with respect to Reidemeister moves I and III},
author = {Kishin Sasaki},
journal= {arXiv preprint arXiv:2205.06490},
year = {2023}
}