A critical point analysis of Landau-Ginzburg potentials with bulk in Gelfand-Cetlin systems

Abstract

© 2021 by Kyoto University.Using the bulk deformation of Floer cohomology by Schubert classes and non-Archimedean analysis of Fukaya-Oh-Ohta-Ono's bulk-deformed potential function, we prove that every complete flag manifold Fl(n) (n ≥ 3) with a monotone Kirillov-Kostant-Souriau (KKS) symplectic form carries a continuum of nondisplaceable Lagrangian tori which degenerates to a nontorus fiber in the Hausdorff limit. In particular, the Lagrangian S3-fiber in Fl(3) is nondisplaceable, answering a question raised by Nohara and Ueda who computed its Floer cohomology to be vanishing.