Virtual unknotting numbers of certain virtual torus knots

Masaharu Ishikawa, Hirokazu Yanagi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the (p,q)-torus knot, that is, (p - 1)(q - 1)/2.

Original languageEnglish
Article number1750070
JournalJournal of Knot Theory and its Ramifications
Volume26
Issue number11
DOIs
Publication statusPublished - 2017 Oct 1

Keywords

  • Unknotting number
  • virtual knot

ASJC Scopus subject areas

  • Algebra and Number Theory

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