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The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials. (English) Zbl 0953.57007
The author considers the vector spaces \(H_{n,l}\) and \(F_{n,l}\) spanned by the degree-\(n\) coefficients in power series forms of the Homfly and Kauffman polynomials of links with \(l\) components. Generalizing previously known formulas, the dimensions of the spaces \(H_{n,l}\), \(F_{n,l}\) and \(H_{n,l}+F_{n,l}\) for all values of \(n\) and \(l\) are determined. Furthermore, the author shows that for knots the algebra generated by \(\bigoplus_n H_{n,1}+F_{n,1}\) is a polynomial algebra with \(\dim(H_{n,1}+F_{n,1})-1=n+[n/2]-4\) generators in degree \(n\geq 4\) and one generator in degrees \(2\) and \(3\). The author takes care to briefly define the various knot and link polynomials, in addition the article contains a long and useful list of references.

MSC:
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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