Craig Westerland : Homology of stabilized moduli of Lefschetz fibrations

Abstract: This talk is about the space of relatively minimal Lefschetz fibrations over surfaces X with at most one node in each fibre. We study the homology of these spaces as the number of nodal fibres tends to infinity, and relate the stable homology to the homology of the function space of maps from X to a variant of the Deligne-Mumford compactification of M_g. Restricting our answer to H_0 yields a form of Auroux's stable classification of Lefschetz vibrations.