On crossing changes for surface-knots

Amal Al Kharusi, Tsukasa Yashiro

Research output: Contribution to journalArticle

Abstract

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.

Original languageEnglish
Pages (from-to)1247-1257
Number of pages11
JournalKyungpook Mathematical Journal
Volume56
Issue number4
DOIs
Publication statusPublished - 2016

Fingerprint

Knot
Curve
Diagram
Invariant

Keywords

  • Crossing changes
  • Invariant
  • Roseman moves
  • Surface-knot

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On crossing changes for surface-knots. / Al Kharusi, Amal; Yashiro, Tsukasa.

In: Kyungpook Mathematical Journal, Vol. 56, No. 4, 2016, p. 1247-1257.

Research output: Contribution to journalArticle

Al Kharusi, Amal ; Yashiro, Tsukasa. / On crossing changes for surface-knots. In: Kyungpook Mathematical Journal. 2016 ; Vol. 56, No. 4. pp. 1247-1257.
@article{808c1962e80f4ec1a503e13cc2f2bf14,
title = "On crossing changes for surface-knots",
abstract = "In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.",
keywords = "Crossing changes, Invariant, Roseman moves, Surface-knot",
author = "{Al Kharusi}, Amal and Tsukasa Yashiro",
year = "2016",
doi = "10.5666/KMJ.2016.56.4.1247",
language = "English",
volume = "56",
pages = "1247--1257",
journal = "Kyungpook Mathematical Journal",
issn = "1225-6951",
publisher = "Kyungpook National University",
number = "4",

}

TY - JOUR

T1 - On crossing changes for surface-knots

AU - Al Kharusi, Amal

AU - Yashiro, Tsukasa

PY - 2016

Y1 - 2016

N2 - In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.

AB - In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.

KW - Crossing changes

KW - Invariant

KW - Roseman moves

KW - Surface-knot

UR - http://www.scopus.com/inward/record.url?scp=85014931875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014931875&partnerID=8YFLogxK

U2 - 10.5666/KMJ.2016.56.4.1247

DO - 10.5666/KMJ.2016.56.4.1247

M3 - Article

VL - 56

SP - 1247

EP - 1257

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

SN - 1225-6951

IS - 4

ER -