Release Time:2022-06-19  Hits:

Date of Publication: 2019-01-01

Journal: Chinese Annals of Mathematics, Ser. A

Volume: 40

Issue: 4

Page Number: 443-448

ISSN: 1000-8314

Key Words: "$n$-Move; Knot; $n$-Move; $n$-Gordian distance; $n$-Gordian complex"

CN: 31-1328/O1

Abstract: In this paper,the $n$-Gordian complex of knots is defined which is an extention of the Gordian complex of knots.The authors show that if $n \ge 2$ and $n$ is even,then for any knot $K$ and any positive integer $r$,there is a finite set of knots of size $r$ containing $K$,such that the $n$-Gordian distance between any two knots in this set is 1.

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