## 抄録

A local move is a pair of tangles with same end points. Habiro defined a system of local moves, C_{n}-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 C_{n}-moves. We define a local move, β_{n}-move, which is obtained from a C_{n}-move by duplicating a single pair of arcs with same end points. Then we immediately have that a C_{n}+1-move is realized by a β_{n}-move and that a β_{n},-move is realized by twice C_{n}-moves. In this note we study the relation between C_{n}-move and β _{n}-move, and in particular, give answers to the following questions: (1) Is a β_{n}-move realized by a finite sequence of C _{n}+1-moves? (2) Is C_{n}-move realized by a finite sequence of β_{n},-moves?

本文言語 | English |
---|---|

ページ（範囲） | 839-851 |

ページ数 | 13 |

ジャーナル | Journal of Knot Theory and its Ramifications |

巻 | 15 |

号 | 7 |

DOI | |

出版ステータス | Published - 2006 9月 |

外部発表 | はい |

## ASJC Scopus subject areas

- 代数と数論

## フィンガープリント

「C_{n}-move and its duplicated move of links」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。