Fukaya category

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.


This article is issued from Wikipedia - version of the 10/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.