Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-fre...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148630 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546089239904256 |
|---|---|
| author | Salazar, M.A. Sepe, D. |
| author_facet | Salazar, M.A. Sepe, D. |
| citation_txt | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones.
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| first_indexed | 2025-11-25T10:19:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148630 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T10:19:54Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Salazar, M.A. Sepe, D. 2019-02-18T16:46:28Z 2019-02-18T16:46:28Z 2017 Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D10; 53D17; 53D20; 37J15 DOI:10.3842/SIGMA.2017.033 https://nasplib.isofts.kiev.ua/handle/123456789/148630 Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones. This paper is a contribution to the Special Issue “Gone Fishing”. The full collection is available at
 http://www.emis.de/journals/SIGMA/gone-fishing2016.html.
 We would like to thank two anonymous referees for the suggestions that helped improve significantly the content and its presentation. Furthermore, we would like to thank Camilo Arias
 Abad for interesting conversations. M.A.S. would like to thank IMPA, CRM and MPIM Bonn
 for hospitality at various stages of the project. M.A.S. was partly supported by the DevMath
 programme of the Centre de Recerca Matem`atica and by the Max Planck Institute for Mathematics in Bonn. D.S. was partly supported by ERC starting grant 279729, by the NWO Veni
 grant 639.031.345 and by CNPq. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators Article published earlier |
| spellingShingle | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators Salazar, M.A. Sepe, D. |
| title | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_full | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_fullStr | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_full_unstemmed | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_short | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_sort | contact isotropic realisations of jacobi manifolds via spencer operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148630 |
| work_keys_str_mv | AT salazarma contactisotropicrealisationsofjacobimanifoldsviaspenceroperators AT seped contactisotropicrealisationsofjacobimanifoldsviaspenceroperators |