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Gauss diagram formulas for Vassiliev invariants. (English) Zbl 0851.57010
A Gauss diagram is an oriented circle with a finite number of oriented, signed chords. A regular projection of an oriented knot, viewed as an immersion of an oriented circle in the plane, determines a Gauss diagram in which the preimages of double points are connected by chords oriented from the upper point to the lower one, and each chord is signed by the local writhe at the double point. This paper presents simple formulae in terms of such Gauss diagrams for higher Vassiliev invariants, generalizing combinatorial versions of the Gauss integral formula for the linking number.

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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