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 the -move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation -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 -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}
}