# 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.