Sergei Lando: Graph invariants producing knot invariants

Povzetek.

A class of graph invariants, called 4-invariants, is discussed. These invariants satisfy certain relations, called the 4-term relations. The latter look similar to the famous deletion/contraction relations. The corresponding Hopf algebra of 4-invariants is similar to the ring of graphs introduced by W. T. Tutte in 1946, but its structure is more complicated. The roots of the definition are in low dimensional topology, namely, in the recent theory of Vassiliev knot invariants. In particular, 4-invariants of graphs determine Vassiliev invariants of knots. The relation between the two notions is discussed.