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

By Cheol-Hyun Cho. 2007

49 citations recorded by the source corpus.

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 a toric Fano manifold (which was also proven by Entov and Polterovich via the theory of symplectic quasi-states) and 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d54a14212bb299bbc2b5910e41262920a61452ef

How researchers see this paper

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In Applied Mathematics

1. O. Cornea
2. Cheol-Hyun Cho
3. Michael Usher
4. P. Biran
5. Hansol Hong
6. Urs Frauenfelder
7. I. Smith
8. E. Shelukhin

In Geometry and Topology

1. O. Cornea
2. P. Biran
3. Michael Usher
4. Cheol-Hyun Cho
5. Siu-Cheong Lau
6. Hansol Hong
7. L. Polterovich
8. E. Shelukhin

In Mathematical Physics

1. O. Cornea
2. Michael Usher
3. P. Biran
4. Cheol-Hyun Cho
5. Siu-Cheong Lau
6. Hansol Hong
7. L. Polterovich
8. E. Shelukhin

Citations in the corpus

• Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms (2010, methodology): “Choose a homogeneous basis ∆1, . . . ,∆N for ⊕ n−1 i=0 H2i(M ;Z)/torsion, with ∆1, . . . ,∆s (for some s < N) a basis for H2n−2(M ;Z)/torsion.”
• Lagrangian topology and enumerative geometry (2010, background): “Versions of the moduli spaces W2 have already been considered by Cho [Cho3].”
• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c} (2013, background): “In the toric case, the filtration zero part was interpreted as holonomy contribution of the associated complex line bundle to overcome this issue ([Cho08],[FOOO10b]).”
• Cyclic symmetry and adic convergence in Lagrangian Floer theory (2009, unknown): “Using the techinique of [3], we can relax the condition x ≡ 0 mod Λ0,nov to x ≡ 0 ∈ H(1)(L; Λ0,nov).”