Obstructions for Symplectic Lie Algebroids
Several types of generically nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, ᵏ-, scattering, and elliptic-log Poisson structures. In this paper, we discuss topolo...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211098 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Obstructions for Symplectic Lie Algebroids. Ralph L. Klaasse. SIGMA 16 (2020), 121, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635533173260288 |
|---|---|
| author | Klaasse, Ralph L. |
| author_facet | Klaasse, Ralph L. |
| citation_txt | Obstructions for Symplectic Lie Algebroids. Ralph L. Klaasse. SIGMA 16 (2020), 121, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Several types of generically nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, ᵏ-, scattering, and elliptic-log Poisson structures. In this paper, we discuss topological obstructions to the existence of such Poisson structures, obtained through the characteristic classes of their associated symplectic Lie algebroids. In particular, we obtain the full obstructions for surfaces to carry such Poisson structures.
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| first_indexed | 2026-03-14T23:13:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211098 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T23:13:47Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Klaasse, Ralph L. 2025-12-23T13:14:26Z 2020 Obstructions for Symplectic Lie Algebroids. Ralph L. Klaasse. SIGMA 16 (2020), 121, 13 pages 1815-0659 2020 Mathematics Subject Classification: 53D17; 53D05 arXiv:1811.05084 https://nasplib.isofts.kiev.ua/handle/123456789/211098 https://doi.org/10.3842/SIGMA.2020.121 Several types of generically nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, ᵏ-, scattering, and elliptic-log Poisson structures. In this paper, we discuss topological obstructions to the existence of such Poisson structures, obtained through the characteristic classes of their associated symplectic Lie algebroids. In particular, we obtain the full obstructions for surfaces to carry such Poisson structures. This work is partially based on [14, Chapter 11], and was supported by ERC consolidator grant 646649 "SymplecticEinstein", and by VIDI grant 639.032.221 from NWO, the Netherlands Organisation for Scientific Research. The author would like to thank Gil Cavalcanti for useful discussions and the anonymous referees for their suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Obstructions for Symplectic Lie Algebroids Article published earlier |
| spellingShingle | Obstructions for Symplectic Lie Algebroids Klaasse, Ralph L. |
| title | Obstructions for Symplectic Lie Algebroids |
| title_full | Obstructions for Symplectic Lie Algebroids |
| title_fullStr | Obstructions for Symplectic Lie Algebroids |
| title_full_unstemmed | Obstructions for Symplectic Lie Algebroids |
| title_short | Obstructions for Symplectic Lie Algebroids |
| title_sort | obstructions for symplectic lie algebroids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211098 |
| work_keys_str_mv | AT klaasseralphl obstructionsforsymplecticliealgebroids |