@article{bd1df6a646ff4dae999b9d3854db8021,
title = "Generalized virtualization on welded links",
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.",
keywords = "Alexander polynomial, Arrow calculus, Associated core group, Multiplexing of crossings, Unknotting operation, Virtualization, Welded knot, Welded link",
author = "Miyazawa, {Haruko A.} and Kodai Wada and Akira Yasuhara",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary 57M25; Secondary 57M27. Key Words and Phrases. welded knot, welded link, virtualization, unknotting operation, arrow calculus, Alexander polynomial, associated core group, multiplexing of crossings. 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). 1For simplicity, we do not use here the usual drawing convention for virtual crossings, which is a small circle around the corresponding double point. Publisher Copyright: {\textcopyright} 2020 The Mathematical Society of Japan",
year = "2020",
doi = "10.2969/JMSJ/82248224",
language = "English",
volume = "72",
pages = "923--944",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "3",
}