Singular Reduction of Generalized Complex Manifolds
In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Li...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146509 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713178714013696 |
|---|---|
| author | Goldberg, T.E. |
| author_facet | Goldberg, T.E. |
| citation_txt | Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for the reduction of Hamiltonian generalized Kähler manifolds.
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| first_indexed | 2025-12-07T17:42:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146509 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:42:28Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Goldberg, T.E. 2019-02-09T19:37:49Z 2019-02-09T19:37:49Z 2010 Singular Reduction of Generalized Complex Manifolds / T.E. Goldberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D20; 53D18; 53C15 DOI:10.3842/SIGMA.2010.081 https://nasplib.isofts.kiev.ua/handle/123456789/146509 In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for the reduction of Hamiltonian generalized Kähler manifolds. The author would like to thank Reyer Sjamaar for his help in understanding the singular reduction in the symplectic case, Yi Lin for several extremely helpful conversations, Tomoo Matsumura for introducing him to generalized complex geometry, the referees for many useful suggestions, and his family and friends for their unwavering support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singular Reduction of Generalized Complex Manifolds Article published earlier |
| spellingShingle | Singular Reduction of Generalized Complex Manifolds Goldberg, T.E. |
| title | Singular Reduction of Generalized Complex Manifolds |
| title_full | Singular Reduction of Generalized Complex Manifolds |
| title_fullStr | Singular Reduction of Generalized Complex Manifolds |
| title_full_unstemmed | Singular Reduction of Generalized Complex Manifolds |
| title_short | Singular Reduction of Generalized Complex Manifolds |
| title_sort | singular reduction of generalized complex manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146509 |
| work_keys_str_mv | AT goldbergte singularreductionofgeneralizedcomplexmanifolds |