In Mirror symmetry, it is expected that Lagrangian submanifold and Floer homology plays a similar role in the symplectic geometry side to the coherent sheaves and sheaf cohomology in complex side. However the presence of "quantum effect" makes the story in the simplex geometry side harder (or more involved). I would like to explain several aspects on the points required to construct basic structures in the symplectic geoemtry side of the story.
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