Commentarii Mathematici Helvetici


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Volume 72, Issue 1, 1997, pp. 110–127
DOI: 10.1007/PL00000362

Published online: 1997-03-31

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

Jens Lieberum[1]

(1) Universit├Ąt Basel, Switzerland

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 $ n \geq 2 $, the n-th order Vassiliev invariant un, defined by $ J_{e^x}(K) = \sum_{n = 0}^{\infty}u_n(K)x^n $, is a polynomial of degree 2n in the gleams.

Keywords: Vassiliev invariants, shadows, gleams, knots, Jones polynomial

Lieberum Jens: For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams. Comment. Math. Helv. 72 (1997), 110-127. doi: 10.1007/PL00000362