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

Abstract

Using the bulk-deformation of Floer cohomology by Schubert cycles 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 symplectic form carries a continuum of non-displaceable Lagrangian tori which degenerates to a non-torus fiber in the Hausdorff limit. In particular, the Lagrangian $S^3$-fiber in $\mathrm{Fl}(3)$ is non-displaceable, answering the question of which was raised by Nohara--Ueda who computed its Floer cohomology to be vanishing.

arXiv comment30 pages, 6 figures, Following a journal editors' suggestion, we split our previous posting arXiv:1704.07213. This article is a revised and improved version of Part 2 of arXiv:1704.07213

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• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle
• Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1
• Lagrangian fibers of Gelfand-Cetlin systems
• Kuranishi structure, Pseudo-holomorphic curve, and virtual fundamental chain: Part 2

Cited by in corpus (1)

• Displacement energy of Lagrangian 3-spheres