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CLASPER-MOVES AMONG RIBBON 2-KNOTS CHARACTERIZING THEIR FINITE TYPE INVARIANTS.

Authors :
WATANABE, TADAYUKI
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