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Fukaya category and Fourier transform

Dmitry Arinkin·Alexander Polishchuk
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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.

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Dmitry Arinkin, Alexander Polishchuk. 1999-06-18. Fukaya category and Fourier transform. https://arxiv.org/abs/math/9811023

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