Virtualized Delta moves for virtual knots and links

Takuji Nakamura; Yasutaka Nakanishi; Shin Satoh; Kodai Wada

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arXiv · 2401.12506

Virtualized Delta moves for virtual knots and links

Takuji Nakamura·Yasutaka Nakanishi·Shin Satoh·Kodai Wada

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Abstract

We introduce a local deformation called the virtualized $\Delta$-move for virtual knots and links. We prove that the virtualized $\Delta$-move is an unknotting operation for virtual knots. Furthermore we give a necessary and sufficient condition for two virtual links to be related by a finite sequence of virtualized $\Delta$-moves.

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Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh, Kodai Wada. 2024-01-23. Virtualized Delta moves for virtual knots and links. https://arxiv.org/abs/2401.12506

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