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December 2009 $SC_n$-moves and the $(n+1)$-st Coefficients of the Conway Polynomials of Links
Haruko Aida MIYAZAWA
Tokyo J. Math. 32(2): 395-408 (December 2009). DOI: 10.3836/tjm/1264170238

Abstract

A local move called a $C_n$-move is related to Vassiliev invariants. It is known that two knots are related by $C_n$-moves if and only if they have the same values of Vassiliev invariants of order less than $n$. In the link case, it is shown that a $C_n$-move does not change the values of any Vassiliev invariants of order less than $n$. It is also known that, if two links can be transformed into each other by a $C_n$-move, then the $n$-th coefficients of the Conway polynomials of them, which are Vassiliev invariants of order $n$, are congruent to each other modulo $2$. An $SC_n$-move is defined as a special $C_n$-move. It is shown that an $SC_n$-move does not change the values of any Vassiliev invariants of links of order less than $n+1$. In this paper, we consider the difference of the $(n+1)$-st coefficients of the Conway polynomials of two links which can be transformed into each other by an $SC_n$-move.

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Haruko Aida MIYAZAWA. "$SC_n$-moves and the $(n+1)$-st Coefficients of the Conway Polynomials of Links." Tokyo J. Math. 32 (2) 395 - 408, December 2009. https://doi.org/10.3836/tjm/1264170238

Information

Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1197.57010
MathSciNet: MR2589951
Digital Object Identifier: 10.3836/tjm/1264170238

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

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Vol.32 • No. 2 • December 2009
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