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CLASPER-MOVES AMONG RIBBON 2-KNOTS CHARACTERIZING THEIR FINITE TYPE INVARIANTS.
- Source :
-
Journal of Knot Theory & Its Ramifications . Nov2006, Vol. 15 Issue 9, p1163-1199. 37p. - Publication Year :
- 2006
-
Abstract
- Habiro found in his thesis a topological interpretation of finite type invariants of knots in terms of local moves called Habiro's Ck-moves. Ck-moves are defined by using his claspers. In this paper we define "oriented" claspers and RCk-moves among ribbon 2-knots as modifications of Habiro's notions to give a similar interpretation of Habiro–Kanenobu–Shima's finite type invariants of ribbon 2-knots. It works also for ribbon 1-knots. Furthermore, by using oriented claspers for ribbon 1-knots, we can prove Habiro–Shima's conjecture in the case of ℚ-valued invariants, saying that ℚ-valued Habiro–Kanenobu–Shima finite type invariant and ℚ-valued Vassiliev–Goussarov finite type invariant are the same thing. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 15
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 23480214
- Full Text :
- https://doi.org/10.1142/S0218216506005056