University of Toronto's Symplectic Geometry Seminar

February 1, 2010, 2:10 pm
Bahen 6183

Joseph Johns

New York University

Lefschetz fibrations on cotagent bundles and Fukaya categories


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.