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

2023/08/03 by Kim, Yoosik
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2308.01636

Abstract

We prove that the two-step flag variety Fℓ(1,n;n+1) carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to S³ × T^2n-4 and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when n > 2.

Related

• Lagrangian fibers of Gelfand-Cetlin systems
• Displacing Lagrangians in the manifolds of full flags in C³
• Lagrangian fibers of Gelfand-Cetlin systems
• Floer cohomologies of non-torus fibers of the Gelfand-Cetlin system
• A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems