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arXiv · 1911.04302

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

Yunhyung Cho·Yoosik Kim·Yong-Geun Oh
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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 $\mathrm{Fl}(n)$ ($n \geq 3$) 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.

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Yunhyung Cho, Yoosik Kim, Yong-Geun Oh. 2019-11-11. A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems. https://arxiv.org/abs/1911.04302

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