On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies
We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic manifold to the bundle of frames. This is a by-produ...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2018 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209435 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies / A. Czarnecki // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735646108418048 |
|---|---|
| author | Czarnecki, A. |
| author_facet | Czarnecki, A. |
| citation_txt | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies / A. Czarnecki // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic manifold to the bundle of frames. This is a by-product of a failed attempt to prove certain finiteness theorems for basic symplectic cohomologies. In the last part of the paper, we include a valid proof.
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| first_indexed | 2025-12-07T19:49:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:49:56Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Czarnecki, A. 2025-11-21T18:49:34Z 2018 On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies / A. Czarnecki // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C12; 57R18 arXiv: 1703.08279 https://nasplib.isofts.kiev.ua/handle/123456789/209435 https://doi.org/10.3842/SIGMA.2018.029 We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic manifold to the bundle of frames. This is a by-product of a failed attempt to prove certain finiteness theorems for basic symplectic cohomologies. In the last part of the paper, we include a valid proof. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies Article published earlier |
| spellingShingle | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies Czarnecki, A. |
| title | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies |
| title_full | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies |
| title_fullStr | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies |
| title_full_unstemmed | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies |
| title_short | On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies |
| title_sort | on the symplectic structures in frame bundles and the finite dimension of basic symplectic cohomologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209435 |
| work_keys_str_mv | AT czarneckia onthesymplecticstructuresinframebundlesandthefinitedimensionofbasicsymplecticcohomologies |