CF-moves for virtual links

Kodai Wada

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arXiv · 2102.12930

CF-moves for virtual links

Kodai Wada

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Abstract

Oikawa defined an unknotting operation on virtual knots, called a CF-move, and gave a classification of 2-component virtual links up to CF-moves by the virtual linking number and his $n$-invariant. In particular, it was proved that a CF-move characterizes the information contained in the virtual linking number for 2-component odd virtual links. In this paper, we extend this result by classifying odd virtual links and almost odd virtual links with arbitrary number of components up to CF-moves, using the virtual linking number. Moreover, we extend Oikawa's $n$-invariant and introduce two invariants for 3-component even virtual links. Using these invariants together with the virtual linking number, we classify 3-component even virtual links up to CF-moves. As a result, a classification of 3-component virtual links up to CF-moves is provided.

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BibTeX RIS

Kodai Wada. 2021-02-25. CF-moves for virtual links. https://arxiv.org/abs/2102.12930

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