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
Externally publishedYes

Fingerprint

Unknotting number
Virtual Knot
Torus knot
Unknot
Diagram

Keywords

  • Unknotting number
  • virtual knot

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Virtual unknotting numbers of certain virtual torus knots. / Ishikawa, Masaharu; Yanagi, Hirokazu.

In: Journal of Knot Theory and its Ramifications, Vol. 26, No. 11, 1750070, 01.10.2017.

Research output: Contribution to journalArticle

@article{6bb3dab1a2be47469afa33ea078ebc0b,
title = "Virtual unknotting numbers of certain virtual torus knots",
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.",
keywords = "Unknotting number, virtual knot",
author = "Masaharu Ishikawa and Hirokazu Yanagi",
year = "2017",
month = "10",
day = "1",
doi = "10.1142/S0218216517500705",
language = "English",
volume = "26",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "11",

}

TY - JOUR

T1 - Virtual unknotting numbers of certain virtual torus knots

AU - Ishikawa, Masaharu

AU - Yanagi, Hirokazu

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Unknotting number

KW - virtual knot

UR - http://www.scopus.com/inward/record.url?scp=85027520468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027520468&partnerID=8YFLogxK

U2 - 10.1142/S0218216517500705

DO - 10.1142/S0218216517500705

M3 - Article

AN - SCOPUS:85027520468

VL - 26

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 11

M1 - 1750070

ER -