Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-08-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: SCIE

Volume: 27

Issue: 9,SI

ISSN: 0218-2165

Key Words: Pass-move; (sic)-move; (sic)over-bar-move; H(n)-move; Gordian distance; Gordian complex

Abstract: In this paper, the <((sic))over bar>-move is defined. We show that for any knot K-0, there exists an infinite family of knots {K-0, K-1, . . .} such that the Gordian distance d(K-i, K-j) = 1 and pass-move-Gordian distance d(p)(K-i, K-j) = 1 for any i not equal j. We also show that there is another infinite family of knots {K-0', K-1', . . .} (where K-0' = K-0) such that the <((sic))over bar>-move-Gordian distance d(<((sic))over bar>)-(K-i', K-j') = 1 and H(n)-Gordian distance d(H(n)) (K-i', K-j') = 1 for any i not equal j and all n >= 2.