English

The H(n)-move is an unknotting operation for virtual and welded links

Geometric Topology 2025-10-22 v2

Abstract

An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that for all n2n \geq 2 the H(n)H(n)-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation H(n)H(n)-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and H(n)H(n)-moves.

Keywords

Cite

@article{arxiv.2211.00459,
  title  = {The H(n)-move is an unknotting operation for virtual and welded links},
  author = {Danish Ali and Zhiqing Yang and Abid Hussain and Mohd Ibrahim Sheikh},
  journal= {arXiv preprint arXiv:2211.00459},
  year   = {2025}
}