Lagrangian Floer theory in symplectic fibrations

Consider a fibration of compact symplectic manifolds F → E → B with a compatible symplectic form on E, and an induced fibration of Lagrangian submanifolds LF → L → LB. We develop a Leray-Serre type spectral sequence to compute the Floer cohomology of L in terms of the Floer complex of LF and LB when F is symplectically small. Moreover, we write down a formula for the leading order superpotential when F is a Kahler homogeneous space. To solve the transversality and compactness problem, we use the classical approach in addition to the perturbation scheme recently developed by Cieliebak-Mohnke [CM07] and Charest-Woodward [CWb; CWa]. As applications, we find Floer-non-trivial tori in complex flag manifolds and ruled surfaces.Ph.D.Includes bibliographical referencesby Douglas Schult