Lieberum, Jens

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

Doc. Math., J. DMV 5, 275-299 (2000)

Summary

Summary: We consider vector spaces $\Hvnl$ and $\Fvnl$ spanned by the degree-$n$ coefficients in power series forms of the Homfly and Kauffman polynomials of links with $\ell$ components. Generalizing previously known formulas, we determine the dimensions of the spaces $\Hvnl, \Fvnl$ and $\Hvnl+\Fvnl$ for all values of $n$ and $\ell$. Furthermore, we show that for knots the algebra generated by $\bigoplus_n \Hvne+\Fvne$ is a polynomial algebra with $\dim(\Hvne+\Fvne)-1=n+[n/2]-4$ generators in degree $n\geq 4$ and one generator in degrees 2 and 3.

Mathematics Subject Classification

57M25

Keywords/Phrases

Vassiliev invariants, link polynomials, Brauer algebra, vogelś algebra, dimensions

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