Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids
In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In the modular case, this result appeared in [Kosmann-Schwarzb...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209880 |
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| Cite this: | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids / P. Frejlich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727741924704256 |
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| author | Frejlich, P. |
| author_facet | Frejlich, P. |
| citation_txt | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids / P. Frejlich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In the modular case, this result appeared in [Kosmann-Schwarzbach Y., Laurent-Gengoux C., Weinstein A., Transform. Groups 13 (2008), 727-755], and with a connectivity assumption which we here show to be unnecessary, it appeared in [Crainic M., Comment. Math. Helv. 78 (2003), 681-721] and [Ginzburg V.L., J. Symplectic Geom. 1 (2001), 121-169].
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| first_indexed | 2025-12-07T19:04:40Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209880 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:04:40Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
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| spelling | Frejlich, P. 2025-11-28T09:40:50Z 2018 Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids / P. Frejlich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D17; 57R20 arXiv: 1805.00542 https://nasplib.isofts.kiev.ua/handle/123456789/209880 https://doi.org/10.3842/SIGMA.2018.124 In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In the modular case, this result appeared in [Kosmann-Schwarzbach Y., Laurent-Gengoux C., Weinstein A., Transform. Groups 13 (2008), 727-755], and with a connectivity assumption which we here show to be unnecessary, it appeared in [Crainic M., Comment. Math. Helv. 78 (2003), 681-721] and [Ginzburg V.L., J. Symplectic Geom. 1 (2001), 121-169]. Work partially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Vrije Competitie grant "Flexibility and Rigidity of Geometric Structures" 612.001.101) and by IMPA (CAPES-FORTAL project). I would like to thank Ioan Mărcut¸, Ori Yudilevich, Rui Loja Fernandes, Olivier Brahic, and David Martínez-Torres. I am also grateful to the anonymous referees for their many useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids Article published earlier |
| spellingShingle | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids Frejlich, P. |
| title | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids |
| title_full | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids |
| title_fullStr | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids |
| title_full_unstemmed | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids |
| title_short | Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids |
| title_sort | morita invariance of intrinsic characteristic classes of lie algebroids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209880 |
| work_keys_str_mv | AT frejlichp moritainvarianceofintrinsiccharacteristicclassesofliealgebroids |