University of Toronto's Symplectic Geometry Seminar

May 21, 2007, 2:10pm
BA 6183

Joseph Johns

Courant Institute

Fukaya categories of Morse Complexifications

Abstract: Given a self indexing Morse function f:N ---> R with three critical values we give an explicit description of a Lefschetz fibration pi: E ---> C, where E is homotopy equivalent to N and this fibration is conjecturally a model for the complexification f_C: D_r(T^*N) ---> C. The main theorem is that the directed Seidel-Fukaya category of pi is isomorphic to the flow category of f, at the level of homology. If time permits we will discuss work in progress on applications to the study of exact Lagrangian submanifolds in T^*N.