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ON HABIRO'S C_n–MOVES AND VASSILIEV INVARIANTS OF ORDER n

YOSHIYUKI OHYAMA

Department of Intelligence and Computer Science, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, 466, Japan

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and

TATSUYA TSUKAMOTO

Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku, Tokyo, 169, Japan

Department of Mathematics, The George Washington University, 2201, G Str., Funger Hall, Washington D.C.20052, USA

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https://doi.org/10.1142/S0218216599000031Cited by:19 (Source: Crossref)

Abstract

Recently it has been proved by Habiro that two knots K₁ and K₂ have the same Vassiliev invariants of order less than or equal to n if and only if K₁ and K₂ can be transformed into each other by a finite sequence of C_n+1–moves. In this paper, we show that the difference of the Vassiliev invariants of order n between two knots that can be transformed into each other by a C_n–move is equal to the value of the Vassiliev invariant for a one-branch tree diagram of order n.

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