Characteristic classes and graph homology
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 \(2\), \(3\),