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

TL;DR

This paper extends the concept of the H(n)-move as an unknotting operation from classical knots to virtual and welded links, demonstrating their equivalence to virtualization and forbidden moves.

Contribution

It introduces the extension of H(n)-moves to virtual knots and links and shows these moves can realize virtualization and forbidden moves.

Findings

H(n)-moves are unknotting operations for virtual links.

Virtualization and forbidden moves can be realized by H(n)-moves.

Extension of classical unknotting operations to virtual links.

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 $n \geq 2$ the $H(n)$-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation $H(n)$-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 $H(n)$-moves.