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

Danish Ali; Zhiqing Yang; Abid Hussain; Mohd Ibrahim Sheikh

doi:10.1142/s021821652350061x

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arXiv · 2211.00459

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

Danish Ali·Zhiqing Yang·Abid Hussain·Mohd Ibrahim Sheikh

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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.

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Danish Ali, Zhiqing Yang, Abid Hussain, Mohd Ibrahim Sheikh. 2022-11-01. The H(n)-move is an unknotting operation for virtual and welded links. https://doi.org/10.1142/s021821652350061x

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