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

Abstract

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.