Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle

Abstract

We show that in many examples the non-displaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with non-unitary line bundle. The examples include all monotone Lagrangian torus fibers in toric Fano manifold (which was also proven by Entov and Polterovich via the theory of symplectic quasi-states), some non-monotone Lagrangian torus fibers. We also extend the results by Oh and the author about the computations of Floer cohomology of Lagrangian torus fibers to the case of all toric Fano manifolds, removing the convexity assumption in the previous work.

17pages,1figure, revised version. Chekanov tori case removed

References in corpus (2)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Quantum Structures for Lagrangian Submanifolds

Cited by in corpus (6)

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• Examples of Matrix Factorizations from SYZ
• Moduli of Lagrangian immersions with formal deformations
• Floer homology of fibrations I: Representing flow lines in Moore path spaces