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- W896987430 abstract "The last two authors ([16]) gave solutions for the problem whether a higher derivative of the Conway, Alexander and Jones polynomial at a point is a Vassiliev invariant or not, by using Birman and Lin's result ([2]). For the Q-polynomial it is known that the n-th derivative (a) of the Q-polynomial of a knot K at a is not a Vassiliev invariant if , -2 ([16], [39]), A sequence of knots is called a twist sequence if they differ in a local part of two strands in which is obtained from by adding a full twist for each i. The local transform of two parallel strands with parallel orientation to the k-half twist of the two strands is called the . In this paper we show that, for any positive integer n, is not a Vassiliev invariant and is not a Vassiliev invariant of degree of the Q-polynomial, we give some criterions to detect whether a knot K can be transformed to a knot K' by finitely many , and if so, we give some results on the number of necessary in the transformation." @default.
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- W896987430 date "2004-01-01" @default.
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- W896987430 title "Twist of Knots and the Q-polynomials" @default.
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