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
Datum:2020
1. Verfasser: Klaasse, Ralph L.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
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
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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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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.
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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