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July, 2020 Generalized virtualization on welded links
Haruko A. MIYAZAWA, Kodai WADA, Akira YASUHARA
J. Math. Soc. Japan 72(3): 923-944 (July, 2020). DOI: 10.2969/jmsj/82248224

Abstract

The aim of this paper is to study two local moves $V(n)$ and $V^{n}$ on welded links for a positive integer $n$, which are generalizations of the crossing virtualization. We show that the $V(n)$-move is an unknotting operation on welded knots for any $n$, and give a classification of welded links up to $V(n)$-moves. On the other hand, we give a necessary condition for two welded links to be equivalent up to $V^{n}$-moves. This leads us to show that the $V^{n}$-move is not an unknotting operation on welded knots except for $n = 1$. We also discuss relations among $V^{n}$-moves, associated core groups and the multiplexing of crossings.

Funding Statement

The second author was supported by Grants-in-Aid for JSPS Research Fellow (#17J08186, #19J00006) of the Japan Society for the Promotion of Science. The third author was partially supported by Grant-in-Aid for Scientific Research (C) (#17K05264) of the Japan Society for the Promotion of Science and Waseda University Grant for Special Research Projects (#2018S-077).

Citation

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Haruko A. MIYAZAWA. Kodai WADA. Akira YASUHARA. "Generalized virtualization on welded links." J. Math. Soc. Japan 72 (3) 923 - 944, July, 2020. https://doi.org/10.2969/jmsj/82248224

Information

Received: 1 March 2019; Published: July, 2020
First available in Project Euclid: 28 February 2020

zbMATH: 07257216
MathSciNet: MR4125851
Digital Object Identifier: 10.2969/jmsj/82248224

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 3 • July, 2020
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