In symplectic topology, a discipline within mathematics, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Floer chain groups: . Its finer structure can be described in the language of quasi categories as an A∞-category.
They are named after Kenji Fukaya who introduced the language first in the context of Morse homology, 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. This conjecture has been computationally verified for a number of comparatively simple examples.
- P. Seidel, Fukaya categories and Picard-Lefschetz theory, Zurich lectures in Advanced Mathematics
- Fukaya, Y-G. Oh, H. Ohta, K. Ono, Lagrangian Intersection Floer Theory, Studies in Advanced Mathematics
- The thread on MathOverflow 'Is the Fukaya category "defined"?'