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Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
Інший ID:
2010 Mathematics Subject Classification: 53D10; 53D17; 53D20; 37J15
DOI:10.3842/SIGMA.2017.033
DOI:10.3842/SIGMA.2017.033
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
463
Завантажень:
329
Анотація:
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.
