Holomorphic disks and the disk potential for a fibered Lagrangian

Abstract

We consider a fibered Lagrangian $L$ in a compact symplectic fibration with small monotone fibers, and develop a strategy for lifting $J$-holomorphic disks with Lagrangian boundary from the base to the total space. In case $L$ is a product, we use this machinery to give a formula for the leading order potential and formulate an unobstructedness criteria for the $A_{\infty }$ algebra. We provide some explicit computations, one of which involves finding an embedded 2n+k dimensional submanifold of Floer-non-trivial tori in a 2n+2k dimensional fiber bundle.

Updated funding information. Final version. Appeared in Jour Symplectic Geometry, Vol 19, Num 1. 69 pages, 3 figures

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Cited by in corpus (2)

• A Leray-Serre spectral sequence for Lagrangian Floer theory
• Fukaya categories of blowups