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A Leray–Serre spectral sequence for Lagrangian Floer theory

Douglas Schultz

Algebraic & Geometric Topology 22 (2022) 3171–3248
Abstract

We consider symplectic fibrations as in Guillemin and Sternberg (J. Funct. Anal. 52 (1983) 106–128) and derive a spectral sequence to compute the Floer cohomology of certain fibered Lagrangians sitting inside a compact symplectic fibration with small monotone fibers and a rational base. We show that if the Floer cohomology with field coefficients of the fibered Lagrangian vanishes, then the Floer cohomology with field coefficients of the total Lagrangian also vanishes. We give an application to certain nontorus fibers of the Gelfand–Cetlin system in flag manifolds, and show that their Floer cohomology vanishes.

Keywords
Lagrangian Floer theory, pseudoholomorphic curves
Mathematical Subject Classification 2010
Primary: 53D40
References
Publication
Received: 12 May 2018
Revised: 31 March 2020
Accepted: 28 August 2021
Published: 30 January 2023
Authors
Douglas Schultz
Department of Mathematics
Humboldt-Universität zu Berlin
Berlin
Germany