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Title: Poisson cohomology and canonical homology of Poisson manifolds (English)
Author: Fernández, Marisa
Author: Ibáñez, Raúl
Author: de León, Manuel
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 32
Issue: 1
Year: 1996
Pages: 29-56
Summary lang: English
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Category: math
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Summary: In this paper we present recent results concerning the Lichnerowicz-Poisson cohomology and the canonical homology of Poisson manifolds. (English)
Keyword: Poisson manifolds
Keyword: symplectic manifolds
Keyword: Lichnerowicz-Poisson cohomology
Keyword: coeffective cohomology
Keyword: canonical homology
Keyword: canonical double complex
MSC: 37J99
MSC: 53C15
MSC: 58A12
MSC: 58A14
MSC: 58F05
idZBL: Zbl 0870.53026
idMR: MR1399839
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Date available: 2008-06-06T21:30:06Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/107560
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Reference: [1] L. C. de Andrés M. Fernández M. de León R. Ibáñez J. Mencía: On the coeffective cohomology of compact symplectic manifolds.C. R. Acad. Sci. Paris, 318, Série I, (1994), 231-236. MR 1262902
Reference: [2] K. H. Bhaskara K. Viswanath: Calculus on Poisson manifolds.Bull. London Math. Soc. 20 (1988), 68-72. MR 0916078
Reference: [3] K. H. Bhaskara K. Viswanath: Poisson algebras and Poisson manifolds.Research Notes in Mathematics, 174, Pitman, London, 1988. MR 0960879
Reference: [4] D. E. Blair: Contact manifolds in Riemannian geometry.Lecture Notes in Math., 509, Springer-Verlag, Berlin, 1976. Zbl 0319.53026, MR 0467588
Reference: [5] R. Bott L. W. Tu: Differential Forms in Algebraic Topology.GTM 82, Springer-Verlag, Berlin, 1982. Zbl 0496.55001, MR 0658304
Reference: [6] T. Bouché: La cohomologie coeffective d’une variété symplectique.Bull. Sci. math., 114 (2) (1990), 115-122. MR 1056157
Reference: [7] J. L. Brylinski: A differential complex for Poisson manifolds.J. Differential Geometry 28 (1988), 93-114. Zbl 0634.58029, MR 0950556
Reference: [8] F. Cantrijn M. de León E. A. Lacomba: Gradient vector fields on cosymplectic manifolds.J. Phys. A: Math. Gen., 25, 175-188, (1992). MR 1146381
Reference: [9] D. Chinea M. de León J. C. Marrero: Coeffective cohomology on cosymplectic manifolds.Bull. Sci. math., 119 (1) (1995), 3-20. MR 1313855
Reference: [10] M. Fernández M. J. Gotay A. Gray: Four-dimensional parallelizable symplectic and complex manifolds.Proc. Amer. Math. Soc. 103 (1988), 1209-1212. MR 0955011
Reference: [11] M. Fernández R. Ibáñez M. de León: On a Brylinski Conjecture for Compact Symplectic Manifods.Proceedings of the “Meeting on Quaternionic Structures in Mathematics and Physics”, SISSA, Trieste (Italy), 1994, (to appear). MR 1645773
Reference: [12] M. Fernández R. Ibáñez M. de León: The coeffective cohomology for compact symplectic nilmanifolds.Proceedings of the III Fall Workshop: Differential Geometry and its Applications, Granada, September 19-20, 1994, Anales de Física, Monografías, 2, 1995. pp. 131-144. MR 1357427
Reference: [13] M. Fernández R. Ibáñez M. de León: A Nomizu’s theorem for the coeffective cohomology.To appear in Mathematische Zeitschrift.
Reference: [14] M. Fernández R. Ibáñez M. de León: The canonical spectral sequences for Poisson manifolds.Preprint IMAFF-CSIC, 1995.
Reference: [15] M. Fernández R. Ibáñez M. de León: Harmonic cohomology classes and the first spectral sequence for compact Poisson manifolds.C. R. Acad. Sci. Paris, 322, Série I, 1996. MR 1386474
Reference: [16] Ph. Griffiths J. Harris: Principles of Algebraic Geometry.John Wiley, New York, 1978. MR 0507725
Reference: [17] A. Hattori: Spectral sequence in the de Rham cohomology of fibre bundles.J. Fac. Sci. Univ. Tokyo, (8) Sect. 1 (1960), 289-331. Zbl 0099.18003, MR 0124918
Reference: [18] M.V. Karasev V.P. Maslov: Nonlinear Poisson brackets. Geometry and Quantization.Translations of Mathematical Monographs, vol. 119, American Mathematical Society, Providence, RI, 1993. MR 1214142
Reference: [19] J.L. Koszul: Crochet de Schouten-Nijenhuis et cohomologie.in “Elie Cartan et les Math. d’Aujour d’Hui”, Astérisque hors-série (1985), 251-271. Zbl 0615.58029, MR 0837203
Reference: [20] M. de León P. R. Rodrigues: Methods of Differential Geometry in Analytical Mechanics.North-Holland Math. Ser. 152, Amsterdam, 1989. MR 1021489
Reference: [21] P. Libermann, Ch. M. Marle: Symplectic Geometry and Analytical Mechanics.Kluwer, Dordrecht, 1987. Zbl 0643.53002, MR 0882548
Reference: [22] A. Lichnerowicz: Les variétés de Poisson et les algébres de Lie associées.J. Differential Geometry 12 (1977), 253-300. MR 0501133
Reference: [23] O. Mathieu: Harmonic cohomology classes of symplectic manifolds.Comment. Math. Helvetici 70 (1995), 1-9. Zbl 0831.58004, MR 1314938
Reference: [24] K. Nomizu: On the cohomology of compact homogeneous spaces of nilpotent Lie groups.Annals of Math. 59 (1954), 531-538. Zbl 0058.02202, MR 0064057
Reference: [25] M. S. Raghunatan: Discrete Subgroups of Lie groups.Ergebnisse der Mathematik, 68, Springer-Verlag, Berlin, 1972. MR 0507234
Reference: [26] W. P. Thurston: Some examples of symplectic manifolds.Proc. Amer. Math. Soc., 55 (1976), 467-468. MR 0402764
Reference: [27] I. Vaisman: Lectures on the Geometry of Poisson Manifolds.Progress in Math. 118, Birkhäuser, Basel, 1994. Zbl 0810.53019, MR 1269545
Reference: [28] A. Weinstein: The local structure of Poisson manifolds.J. Differential Geometry 18 (1983), 523-557. Errata et addenda: J. Differential Geometry 22 (1985), 255. Zbl 0524.58011, MR 0723816
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