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 $\mathrm{Fl}(n)$ ($n\ge 3$) 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 $S^3$-fiber in $\mathrm{Fl}(3)$ is nondisplaceable, answering a question raised by Nohara and Ueda who computed its Floer cohomology to be vanishing.