Семинары под руководством М.Э.Казаряна и С.К.Ландо «Комбинаторика инвариантов Васильева» : С.К.Ландо

Chord diagrams can be understood as graphs having a single vertex and embedded into an orientable surface. This construction can be generalized to graphs with arbitrary number of vertices embedded into 2-dimensional surfaces (either orientable or not). For such graphs, 4-term relations similar to that for chord diagrams can be written out. The space of embedded graphs modulo the 4-term relations describes finite order invariants of links (= ``multicomponent knots’’) in the same way as chord diagrams modulo 4-term relations describe finite order invariants of ordinary knots. There is also a way to introduce a Hopf algebra structure, but we will discuss this topic later.