Fukaya Categories as Categorical Morse Homology

Fukaya Categories as Categorical Morse Homology

The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in analogy with Morse homology, the Fukaya category might result from gluing together Fukaya categories of Wei...

Повний опис

Збережено в:
Бібліографічні деталі
Видавець:Інститут математики НАН України
Дата:2014
Автор: Nadler, D.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2014
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/146836
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Цитувати:Fukaya Categories as Categorical Morse Homology / D. Nadler // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ.

Репозиторії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-146836
record_format dspace
spelling irk-123456789-1468362019-02-12T01:25:13Z Fukaya Categories as Categorical Morse Homology Nadler, D. The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in analogy with Morse homology, the Fukaya category might result from gluing together Fukaya categories of Weinstein cells. This can be formalized by a recollement pattern for Lagrangian branes parallel to that for constructible sheaves. Assuming this structure, we exhibit the Fukaya category as the global sections of a sheaf on the conic topology of the Weinstein manifold. This can be viewed as a symplectic analogue of the well-known algebraic and topological theories of (micro)localization. 2014 Article Fukaya Categories as Categorical Morse Homology / D. Nadler // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D37 DOI:10.3842/SIGMA.2014.018 http://dspace.nbuv.gov.ua/handle/123456789/146836 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in analogy with Morse homology, the Fukaya category might result from gluing together Fukaya categories of Weinstein cells. This can be formalized by a recollement pattern for Lagrangian branes parallel to that for constructible sheaves. Assuming this structure, we exhibit the Fukaya category as the global sections of a sheaf on the conic topology of the Weinstein manifold. This can be viewed as a symplectic analogue of the well-known algebraic and topological theories of (micro)localization.
format Article
author Nadler, D.
spellingShingle Nadler, D.
Fukaya Categories as Categorical Morse Homology
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Nadler, D.
author_sort Nadler, D.
title Fukaya Categories as Categorical Morse Homology
title_short Fukaya Categories as Categorical Morse Homology
title_full Fukaya Categories as Categorical Morse Homology
title_fullStr Fukaya Categories as Categorical Morse Homology
title_full_unstemmed Fukaya Categories as Categorical Morse Homology
title_sort fukaya categories as categorical morse homology
publisher Інститут математики НАН України
publishDate 2014
url http://dspace.nbuv.gov.ua/handle/123456789/146836
citation_txt Fukaya Categories as Categorical Morse Homology / D. Nadler // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT nadlerd fukayacategoriesascategoricalmorsehomology
first_indexed 2023-05-20T17:25:46Z
last_indexed 2023-05-20T17:25:46Z
_version_ 1796153271768842240

Схожі ресурси