Vassiliev invariants and knot polynomials
Finite type invariants of knots and links were introduced by V. A. Vassiliev in 1990. Birman and Lin proved that, after a suitable change of variables, coefficients of the MacLaurin series of the quantum knot polynomials are Vassiliev invariants. In the first part of the paper under review, the authors give critera for the derivative of a knot invariant evaluated at a point \(a\) to be a Vassiliev invariant. More precisely a necessary and sufficient condition is given for the \(n\)th derivatives of the Jones and Conway polynomials to be Vassiliev invariants. In the second part the authors introduce two ways for constructing new polynomial invariants from Vassiliev invariants.
scientific article; zbMATH DE number 1879107