ON 4-MOVE EQUIVALENCE CLASSES OF KNOTS AND LINKS OF TWO COMPONENTS

Author:

DABKOWSKI M. K.1,JABLAN S.2,KHAN N. A.3,SAHI R. K.4

Affiliation:

1. Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083, USA

2. The Mathematical Institute, Knez Mihailova 35, P. O. Box 367, 11001 Belgrade, Serbia

3. Department of Mathematic and Information Sciences, University of North Texas at Dallas, Dallas, TX 75241, USA

4. Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA

Abstract

We study equivalence classes of knots and links of 2 components modulo 4-move. We show that all knots up to 12 crossings and knots in the family 6* reduce by 4-moves to the trivial knot. We also prove that links of 2 components with 11 crossings, and links 6* a1.a2.a3.a4.a5.a6 such that ai is a 2-algebraic tangle with no trivial components reduce to either the trivial link or to the Hopf link. For alternating links of 2-components with 12 we show that L reduces by 4-moves to either trivial link or to the Hopf link whenever L is different than 9*.2 : .2 : .2 (or its mirror image). We suggest the alternating link 9*.2 : .2 : .2 with 12 crossings as a potential example to answer the Problem 1.1(iii) in negative.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Jones Polynomial and Kauffman Bracket Polynomial;Universitext;2023-08-14

2. The Gordian complexes of knots given by 4-move;Journal of Knot Theory and Its Ramifications;2023-04

3. The Dabkowski-Sahi invariant and 4-moves for links;Geometriae Dedicata;2023-02-27

4. On Slavik Jablan’s work on 4-moves;Journal of Knot Theory and Its Ramifications;2016-08

5. Invariants of virtual rational moves;Journal of Knot Theory and Its Ramifications;2014-05

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3