A Leray–Serre spectral sequence for Lagrangian Floer theory

Schultz, Douglas

doi:10.2140/agt.2022.22.3171

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A Leray–Serre spectral sequence for Lagrangian Floer theory

Douglas Schultz

Algebraic & Geometric Topology 22 (2022) 3171–3248

DOI: 10.2140/agt.2022.22.3171

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

Volume 22, issue 7 (2022)