Семинары под руководством М.Э.Казаряна и С.К.Ландо. "Комбинаторика инвариантов Васильева". Лекторы: В.Жуков, С.К.Ландо

V.Zhukov, S.K.Lando

Finite type knot invariants can be described in terms of chord diagrams.
To each chord diagram, its intersection graph is associated. This graph is a simple abstract graph, and many graph invariants produce weight systems, whence knot invariants.
A chord diagram can be understood as an oriented embedded graph with a single vertex.
Similarly, embedded graphs with arbitrarily many vertices are used to describe finite type invariants of links (each vertex corresponds to a link component, which is a knot).

However, there is no way (reasonable from the point of view of knot theory) to associate an abstract graph to an arbitrary graph on a surface.
Delta-matroids are combinatorial objects that replace abstract graphs in this situation.