Exotic symplectic manifolds from Lefschetz fibrations

Abstract

In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds.