|
|
| Line 1: |
Line 1: |
| In [[symplectic topology]], a discipline within mathematics, a '''Fukaya category''' of a [[symplectic manifold]] <math>(M, \omega)</math> is a [[Category (mathematics)|category]] <math>\mathcal F (M)</math> whose objects are [[Lagrangian submanifold]]s of <math>M</math>, and [[morphism]]s are [[Floer homology|Floer chain groups]]: <math>\mathrm{Hom} (L_0, L_1) = FC (L_0,L_1)</math>. Its finer structure can be described in the language of [[quasi-category|quasi categories]] as an [[A∞-algebra|''A''<sub>∞</sub>-category]].
| | НАША КОМАНДА<br><br> |
|
| |
|
| They are named after [[Kenji Fukaya]] who introduced the <math>A_\infty</math> language first in the context of [[Morse homology]], and exist in a number of variants. As Fukaya categories are [[A∞-algebra|''A''<sub>∞</sub>-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.
| | КОНСТАНТИН<br>дизайнер <br><br>Я был на Вашем месте, я тоже заказывал [http://kks.by заказать дизайн]. Обращайтесь и я Вас удивлю!<br><br>ЕКАТЕРИНА <br>режиссер <br><br>[http://kks.by/?cat=33 kks.by] Я арт-менеджер и мое любимое дело - это фото-режиссура.<br><br><br>РИЧАРД<br>кот <br><br>Я символ студии и я слежу за работой Кати и Кости.<br><br>http://www.kks.by |
| | |
| ==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 [http://mathoverflow.net/questions/2905/is-the-fukaya-category-defined thread] on [[MathOverflow]] 'Is the Fukaya category "defined"?'
| |
| | |
| [[Category:Symplectic geometry]]
| |
| | |
| {{differential-geometry-stub}}
| |
Latest revision as of 22:55, 7 January 2015
НАША КОМАНДА
КОНСТАНТИН
дизайнер
Я был на Вашем месте, я тоже заказывал заказать дизайн. Обращайтесь и я Вас удивлю!
ЕКАТЕРИНА
режиссер
kks.by Я арт-менеджер и мое любимое дело - это фото-режиссура.
РИЧАРД
кот
Я символ студии и я слежу за работой Кати и Кости.
http://www.kks.by