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...
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| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146836 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fukaya Categories as Categorical Morse Homology / D. Nadler // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ. |
Репозитарії
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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 |
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2023-05-20T17:25:46Z |
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1796153271768842240 |