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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fukaya category ： ウィキペディア英語版 Fukaya category In symplectic topology, a discipline within mathematics, a Fukaya category of a symplectic manifold $(M,\; \backslash omega)$ is a category $\backslash mathcal\; F\; (M)$ whose objects are Lagrangian submanifolds of $M$, and morphisms are Floer chain groups: $\backslash mathrm\; (L\_0,\; L\_1)\; =\; FC\; (L\_0,L\_1)$. 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 $A\_\backslash infty$ 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 a celebrated conjecture of Maxim Kontsevich: the homological mirror symmetry. This conjecture has been verified by computations for a variety of comparatively simple examples. ==References== *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"?' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fukaya category」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.