English

Classification of $2$-component virtual links up to $\Xi$-moves

Geometric Topology 2023-10-20 v2

Abstract

The Ξ\Xi-move is a local move generated by forbidden moves in virtual knot theory. This move was introduced by Taniguchi and the second author, who showed that it characterizes the odd writhe of virtual knots, which is a fundamental invariant defined by Kauffman. In this paper, we extend this result by classifying 22-component virtual links up to Ξ\Xi-moves, using refinements of the odd writhe and linking numbers.

Keywords

Cite

@article{arxiv.2002.08305,
  title  = {Classification of $2$-component virtual links up to $\Xi$-moves},
  author = {Jean-Baptiste Meilhan and Shin Satoh and Kodai Wada},
  journal= {arXiv preprint arXiv:2002.08305},
  year   = {2023}
}

Comments

26 pages, 39 figures; v2: substantial revision. To appear in Fundamenta Mathematicae

R2 v1 2026-06-23T13:47:04.925Z