JournalscmhVol. 72 , No. 1DOI 10.1007/pl00000362

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

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.