Geometry and Topology Seminar

In this talk we'll introduce SL(3) foams and their evaluation to symmetric functions in three variables. This construction gives rise to a functorial homology theory for plane trivalent graphs G. A naive conjecture is that the rank of this homology group assigned to G is the number of Tait colorings of G. A Tait coloring is the coloring of edges of a trivalent graph in three colors such that at each vertex the three edges have different colors. We'll discuss relation of this story to the Kronheimer-Mrowka homology theory and to the four-color theorem.