The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials

Details The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials

1998-06-11

arxiv.org/abs/math/9806064v3

Documenta Mathematica, Vol 5(2000), 275-299

Mathematics

Quantum Algebra

25 pages, 14 figures

Scientific paper

We consider 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, we determine 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. Furthermore, we show that for knots the algebra generated by H(n,1)+F(n,1) (n > 0) is a polynomial algebra with dim(H(n,1)+F(n,1))-1=n+[n/2]-4 generators in degree n>3 and one generator in degrees 2 and 3.

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