Monopole Floer homology for webs and foams

Abstract: Webs are embedded trivalent graphs in the 3-sphere and foams are singular cobordisms between webs. I will talk about a construction of monopoleFloer homology for webs that is functorial under foam cobordisms.  The approach is based on Kronheimer and Mrowka’s monopole Floer homology and the ingredients include both real and orbifold Seiberg-Witten theory. There is an interesting analogy between this monopole web homology and the instanton web homology J^#, introduced by Kronheimer and Mrowka.