Generalized virtualization on welded links

Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)923-944
Number of pages22
JournalJournal of the Mathematical Society of Japan
Volume72
Issue number3
DOIs
Publication statusPublished - 2020

Keywords

  • Alexander polynomial
  • Arrow calculus
  • Associated core group
  • Multiplexing of crossings
  • Unknotting operation
  • Virtualization
  • Welded knot
  • Welded link

ASJC Scopus subject areas

  • Mathematics(all)

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