Shigeyuki Morita

Characteristic classes and graph homology

slide: PDF.
video: comming soon.
We discuss the interaction between the theory of characteristic classes of various geometric structures and that of graph homology due to Kontsevich. More precisely, we consider characteristic classes of moduli spaces of curves, moduli spaces of graphs and those of transversely symplectic foliations, corresponding to associative, lie and commutative versions of graph homology, respectively.
We survey the present state of explicit determination in each case. We then mention the important but extremely difficult problem of enhancing these pictures to the group levels rather than the Lie algebras.
We expect that these enhanced pictures will eventually shed light on certain mysteries in topology of dimensions \(2\), \(3\), and \(4\).