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On the combinatorics of Vassiliev invariants. (English) Zbl 0938.57004

Yang, Chen Ning (ed.) et al., Braid group, knot theory and statistical mechanics II. London: World Scientific. Adv. Ser. Math. Phys. 17, 1-19 (1994).
The author explains how to define Vassiliev invariants combinatorically. Vassiliev invariants are defined in terms of the cohomology of knot spaces by V. A. Vassiliev [Cohomology of knot spaces, in “Theory of singularities and its applications”, Adv. Sov. Mat. 1, 23-69 (1990; Zbl 0727.57008)]. She shows that for a Vassiliev invariant \(v\) of order \(n\), the value for any knot type \({\mathbb K}\) is determined by the values of \(v\) on a finite set of singular knots. The choice of such a finite set of singular knots, and the assignment of a numerical value of \(v\) of the singular knots are known as an actuality table for a Vassiliev invariant of order \(n\). She gives some open problems about Vassiliev invariants.
For the entire collection see [Zbl 0798.00007].
Reviewer: T.Takata (Fukuoka)

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)

Citations:

Zbl 0727.57008
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