LAGRANGIAN FLOER THEORY IN SYMPLECTIC FIBRATIONS Lagrangian Floer theory in symplectic fibrations release_ogslkz244rcgrmlvd4r4blfbfy

Abstract

Consider a fibration of compact symplectic manifolds F → E → B with a compatible symplectic form on E, and an induced fibration of Lagrangian submanifolds L F → L → L B. We develop a Leray-Serre type spectral sequence to compute the Floer cohomology of L in terms of the Floer complex of L F and L B when F is symplectically small. Moreover, we write down a formula for the leading order superpotential when F is a Kähler 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. ii
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