On non-displaceable Lagrangian submanifolds in two-step flag varieties

Yoosik Kim

doi:10.4134/JKMS.j230098

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2023; 60(5): 1109-1133

Online first article August 14, 2023 Printed September 1, 2023

https://doi.org/10.4134/JKMS.j230098

On non-displaceable Lagrangian submanifolds in two-step flag varieties

Yoosik Kim

Pusan National University

Abstract

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Abstract

We prove that the two-step flag variety $\mathcal{F}\ell(1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.

Keywords: Floer cohomology, Gelfand--Zeitlin systems, partial flag manifolds, non-displaceable Lagrangians, potential functions

MSC numbers: Primary 53D40, 53D12, 14M15

Supported by: This work was supported by a 2-Year Research Grant of Pusan National University.