Fukaya category
Category of a symplectic manifold / From Wikipedia, the free encyclopedia
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In symplectic topology, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Lagrangian Floer chain groups: . Its finer structure can be described as an A∞-category.
They are named after Kenji Fukaya who introduced the language first in the context of Morse homology,[1] and exist in a number of variants. As Fukaya categories are A∞-categories, they have associated derived categories, which are the subject of the celebrated homological mirror symmetry conjecture of Maxim Kontsevich.[2] This conjecture has now been computationally verified for a number of examples.