On Vassiliev’s knot invariants. (English) Zbl 0847.57011

Mohnke, Klaus

Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 169-183 (1994).

This article under review is based on a lecture given by P. Cartier.
Some basic results about Vassiliev’s knot invariants (such as chord diagrams, Feynman diagrams, relations to Lie algebras and their representations) are surveyed. The Knizhnik-Zamolodchikov equation and its solution (which gives a representation of the braid group) due to V. G. Drinfel’d are also described. A result of the lecturer about a combinatorial definition of the universal Vassiliev invariant (Kontsevich integral) [P. Cartier, C. R. Acad. Sci., Paris, Sér. I 316, 1205-1210 (1993; Zbl 0791.57006)] is also described very roughly.
Unfortunately the references are too poor to know the origin of the results appearing here.
For the entire collection see [Zbl 0823.00015].

Reviewer: H.Murakami (Tokyo)

MSC:

57M25	Knots and links in the \(3\)-sphere (MSC2010)
17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)

Keywords:

Vassiliev invariant; braid; knot; chord diagram; Knizhnik-Zamolodchikov equation; Kontsevich integral

Citations:

Zbl 0791.57006