Kontsevich invariant

The Kontsevich invariant is defined by monodromy along solutions of the Knizhnik–Zamolodchikov equations.

As is shown in the figure on the right, a Jacobi diagram with order n is the graph with 2n vertices, with the external circle depicted as solid line circle and with dashed lines called inner graph, which satisfies the following conditions: The edges on G are called chords.

The map extended to the space A(X) is also called the weight system.

D. Bar-Natan later formulated them as the 1-3 valued graphs and studied their algebraic properties, and called them "Chinese character diagrams" in his paper.

We can interpret them from a more general point of view by claspers, which were defined independently by Goussarov and Kazuo Habiro in the later half of the 1990s.