Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a knot. In fact, any Vassiliev knot invariant can be derived from it. To construct the Kontsevich integral, represent the three-dimensional space R^3 as a direct product of a complex line C with coordinate z and a real line R with coordinate t. The integral is defined for Morse knots, i.e., knots K embedded in R^3 = C_z×R_t in such a way that the coordinate t is a Morse function on K, and its values belong to the graded completion h^_ c a l A of the algebra of chord diagrams A.

Gauss integral | Morse knot | Vassiliev invariant