Ulrike Tillmann (University of Oxford)
tillmann@maths.ox.ac.uk Just as a complex vector bundle determines cohomology classes (Chern classes) in the base space, so do bundles of surfaces. Mumford constructed a set of tautological classes using integration over fibres. These are rational classes. One can refine Mumford's methods and detect infinite families of torsion classes.
I will review what is known about characteristic classes for surface bundles, including Mumford's construction, before defining a topological version of integration over fibres (transfer map) and describing the new families of torsion classes. (Part of this is joint work with Ib Madsen.)