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Indexed by:期刊论文

Date of Publication:2018-08-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE

Volume:27

Issue:9,SI

ISSN No.: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.