JournalscmhVol. 72, No. 1pp. 110–127

For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams

  • Jens Lieberum

    Universität Basel, Switzerland
For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams cover
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Abstract

We use Turaev's technique of shadows and gleams to parametrize the set of all knots in S 3 with the same Hopf projection. We show that the Vassiliev invariants arising from the Jones polynomial Jt (K) are polynomials in the gleams, i.e., for n2n \geq 2 , the n-th order Vassiliev invariant un, defined by Jex(K)=n=0un(K)xnJ_{e^x}(K) = \sum_{n = 0}^{\infty}u_n(K)x^n , is a polynomial of degree 2n in the gleams.

Cite this article

Jens Lieberum, For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams. Comment. Math. Helv. 72 (1997), no. 1, pp. 110–127

DOI 10.1007/PL00000362