Fukaya category and Fourier transform

Abstract

We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the dual family has a natural complex structure). In the 1-dimensional case the former category is closely related to the Fukaya category.

14 pages, AMSLatex, minor corrections

References in corpus (2)

• The moduli space of special Lagrangian submanifolds
• Special Lagrangian Fibrations II: Geometry

Cited by in corpus (19)

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• Mirror symmetry and actions of braid groups on derived categories
• Symmetries of Lagrangian fibrations
• The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks
• A Fourier transform for sheaves on Lagrangian families of real tori
• Hyper-symplectic structures on integrable systems
• A Fourier-Mukai transform for real torus bundles
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry
• Weak mirror symmetry of Lie algebras
• Twin Lagrangian fibrations in mirror symmetry
• Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces
• Two-dimensional Lagrangian singularities and bifurcations of gradient lines I
• Quantum corrections in mirror symmetry for a 2-dimensional Lagrangian submanifold with an elliptic umbilic
• Remarks on the homological mirror symmetry for tori