Writhes and $2k$-moves for virtual knots

Kodai Wada

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arXiv · 2309.07441

Writhes and $2k$-moves for virtual knots

Kodai Wada

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Abstract

A $2k$-move is a local deformation adding or removing $2k$ half-twists. We show that if two virtual knots are related by a finite sequence of $2k$-moves, then their $n$-writhes are congruent modulo $k$ for any nonzero integer $n$, and their odd writhes are congruent modulo $2k$. Moreover, we give a necessary and sufficient condition for two virtual knots to have the same congruence class of odd writhes modulo $2k$.

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BibTeX RIS

Kodai Wada. 2023-09-14. Writhes and $2k$-moves for virtual knots. https://arxiv.org/abs/2309.07441

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