February 1, 2010, 2:10 pm

Bahen 6183

Abstract:I will describe a construction of certain Lefschetz fibrations on cotagent bundles, which are modeled on complexified Morse functions. I will then describe a general theorem of Seidel, which says that the Lefschetz thimbles of a Lefschetz fibration always generate the derived Fukaya category of the total space (in the triangulated sense). Then I will explain how this theorem applies to the Lefschetz fibrations above. The outcome is that the Fukaya category of the cotagent bundle is described in terms of certain quiver reprentations related to More theory on the base.