Self Ck-move, quasi self Ck-move and the conway potential function for links

Tetsuo Shibuya*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Nakanishi and Shibuya gave a relation between link homotopy and quasi self delta-equivalence. And they also gave a necessary condition for two links to be self delta-equivalent by using the multivariable Alexander polynomial. Link homotopy and quasi self delta-equivalence are also called self C 1-equivalence and quasi self C2-equivalence respectively. In this paper, we generalize their results. In Sec. 1, we give a relation between self Ck-equivalence and quasi self Ck+1- equivalence. In Secs. 2 and 3, we give necessary conditions for two links to be self Ck-equivalent by using the multivariable Conway potential function and the Conway polynomial respectively.

Original languageEnglish
Pages (from-to)877-893
Number of pages17
JournalJournal of Knot Theory and its Ramifications
Issue number7
Publication statusPublished - 2004 Nov 1
Externally publishedYes


  • Alexander polynomial
  • C-move
  • Conway polynomial
  • Delta-move

ASJC Scopus subject areas

  • Algebra and Number Theory


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