Cn-move and its duplicated move of links

Kazuaki Kobayashi, Tetsuo Shibuya, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review

Abstract

A local move is a pair of tangles with same end points. Habiro defined a system of local moves, Cn-moves, and showed that two knots have the same Vassiliev invariants of order ≤ n - 1 if and only if they are transformed into each other by Cn-moves. We define a local move, βn-move, which is obtained from a Cn-move by duplicating a single pair of arcs with same end points. Then we immediately have that a Cn+1-move is realized by a βn-move and that a βn,-move is realized by twice Cn-moves. In this note we study the relation between Cn-move and β n-move, and in particular, give answers to the following questions: (1) Is a βn-move realized by a finite sequence of C n+1-moves? (2) Is Cn-move realized by a finite sequence of βn,-moves?

Original languageEnglish
Pages (from-to)839-851
Number of pages13
JournalJournal of Knot Theory and its Ramifications
Volume15
Issue number7
DOIs
Publication statusPublished - 2006 Sep 1
Externally publishedYes

Keywords

  • C-move
  • Local move
  • Δ-move
  • β-move

ASJC Scopus subject areas

  • Algebra and Number Theory

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