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 , the n-th order Vassiliev invariant un, defined by , is a polynomial of degree 2n in the gleams.
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Jens Lieberum, For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams. Comment. Math. Helv. 72 (1997), no. 1, pp. 110–127DOI 10.1007/PL00000362