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Date of Publication:2019-01-01

Journal:Chinese Annals of Mathematics, Ser. A

Volume:40

Issue:4

Page Number:443-448

ISSN No.:1000-8314

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

CN No.: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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