The H(n)-move is an unknotting operation for virtual and welded links
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914104528076800 |
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| author | Ali, Danish Yang, Zhiqing Hussain, Abid Sheikh, Mohd Ibrahim |
| author_facet | Ali, Danish Yang, Zhiqing Hussain, Abid Sheikh, Mohd Ibrahim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00459 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The H(n)-move is an unknotting operation for virtual and welded links Ali, Danish Yang, Zhiqing Hussain, Abid Sheikh, Mohd Ibrahim Geometric Topology 57K10, 57K12 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. |
| title | The H(n)-move is an unknotting operation for virtual and welded links |
| topic | Geometric Topology 57K10, 57K12 |
| url | https://arxiv.org/abs/2211.00459 |