Journal of Symplectic Geometry

Volume 19 (2021)

Number 1

Holomorphic disks and the disk potential for a fibered Lagrangian

Pages: 143 – 239

DOI: https://dx.doi.org/10.4310/JSG.2021.v19.n1.a4

Author

Douglas Schultz (Department of Mathematics, Humboldt Universität zu Berlin, Germany)

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.

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Received 16 May 2018

Accepted 4 September 2020

Published 26 March 2021