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 language | English |
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Pages (from-to) | 839-851 |
Number of pages | 13 |
Journal | Journal of Knot Theory and its Ramifications |
Volume | 15 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2006 Sep |
Externally published | Yes |
Keywords
- C-move
- Local move
- Δ-move
- β-move
ASJC Scopus subject areas
- Algebra and Number Theory