THE GORDIAN COMPLEX OF KNOTS-Reference-Cited by-同舟云学术

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THE GORDIAN COMPLEX OF KNOTS

Published:2002-05 Issue:03 Volume:11 Page:363-368
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

HIRASAWA MIKAMI¹,UCHIDA YOSHIAKI²

Affiliation:

1. Graduate School of Science, Osaka University, Toyonaka Osaka 560-0043, Japan

2. Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan

Abstract

In this paper, we define the Gordian complex of knots, which is a simplicial complex whose vertices consist of all oriented knot types in the 3-sphere. We show that for any knot K, there exists an infinite family of distinct knots containing K such that any pair (Ki, Kj) of the member of the family, the Gordian distance dG(Ki, Kj) = 1.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216502001676

Reference1 articles.

Cited by 31 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. Cobordism distance on the projective space of the knot concordance group;Canadian Journal of Mathematics;2023-06-27

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

3. Knot graphs and Gromov hyperbolicity;Mathematische Zeitschrift;2022-01-31

4. The Gordian complex of theta-curves;Journal of Knot Theory and Its Ramifications;2021-07

5. The Conway Gordian Graph;CR ACAD BULG SCI;2021-06-29

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