In this paper we present recent results concerning the Lichnerowicz-Poisson cohomology and the canonical homology of Poisson manifolds.
@article{107560, author = {Marisa Fern\'andez and Ra\'ul Ib\'a\~nez and Manuel de Le\'on}, title = {Poisson cohomology and canonical homology of Poisson manifolds}, journal = {Archivum Mathematicum}, volume = {032}, year = {1996}, pages = {29-56}, zbl = {0870.53026}, mrnumber = {1399839}, language = {en}, url = {http://dml.mathdoc.fr/item/107560} }
Fernández, Marisa; Ibáñez, Raúl; de León, Manuel. Poisson cohomology and canonical homology of Poisson manifolds. Archivum Mathematicum, Tome 032 (1996) pp. 29-56. http://gdmltest.u-ga.fr/item/107560/
On the coeffective cohomology of compact symplectic manifolds, C. R. Acad. Sci. Paris, 318, Série I, (1994), 231-236. (1994) | MR 1262902
Calculus on Poisson manifolds, Bull. London Math. Soc. 20 (1988), 68-72. (1988) | MR 0916078
Poisson algebras and Poisson manifolds, Research Notes in Mathematics, 174, Pitman, London, 1988. (1988) | MR 0960879
Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, Springer-Verlag, Berlin, 1976. (1976) | MR 0467588 | Zbl 0319.53026
Differential Forms in Algebraic Topology, GTM 82, Springer-Verlag, Berlin, 1982. (1982) | MR 0658304 | Zbl 0496.55001
La cohomologie coeffective d’une variété symplectique, Bull. Sci. math., 114 (2) (1990), 115-122. (1990) | MR 1056157
A differential complex for Poisson manifolds, J. Differential Geometry 28 (1988), 93-114. (1988) | MR 0950556 | Zbl 0634.58029
Gradient vector fields on cosymplectic manifolds, J. Phys. A: Math. Gen., 25, 175-188, (1992). (1992) | MR 1146381
Coeffective cohomology on cosymplectic manifolds, Bull. Sci. math., 119 (1) (1995), 3-20. (1995) | MR 1313855
Four-dimensional parallelizable symplectic and complex manifolds, Proc. Amer. Math. Soc. 103 (1988), 1209-1212. (1988) | MR 0955011
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). (1994) | MR 1645773
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. (1994) | MR 1357427
A Nomizu’s theorem for the coeffective cohomology, To appear in Mathematische Zeitschrift.
The canonical spectral sequences for Poisson manifolds, Preprint IMAFF-CSIC, 1995. (1995)
Harmonic cohomology classes and the first spectral sequence for compact Poisson manifolds, C. R. Acad. Sci. Paris, 322, Série I, 1996. (1996) | MR 1386474
Principles of Algebraic Geometry, John Wiley, New York, 1978. (1978) | MR 0507725
Spectral sequence in the de Rham cohomology of fibre bundles, J. Fac. Sci. Univ. Tokyo, (8) Sect. 1 (1960), 289-331. (1960) | MR 0124918 | Zbl 0099.18003
Nonlinear Poisson brackets. Geometry and Quantization, Translations of Mathematical Monographs, vol. 119, American Mathematical Society, Providence, RI, 1993. (1993) | MR 1214142
Crochet de Schouten-Nijenhuis et cohomologie, in “Elie Cartan et les Math. d’Aujour d’Hui”, Astérisque hors-série (1985), 251-271. (1985) | MR 0837203 | Zbl 0615.58029
Methods of Differential Geometry in Analytical Mechanics, North-Holland Math. Ser. 152, Amsterdam, 1989. (1989) | MR 1021489
Symplectic Geometry and Analytical Mechanics, Kluwer, Dordrecht, 1987. (1987) | MR 0882548 | Zbl 0643.53002
Les variétés de Poisson et les algébres de Lie associées, J. Differential Geometry 12 (1977), 253-300. (1977) | MR 0501133
Harmonic cohomology classes of symplectic manifolds, Comment. Math. Helvetici 70 (1995), 1-9. (1995) | MR 1314938 | Zbl 0831.58004
On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Annals of Math. 59 (1954), 531-538. (1954) | MR 0064057 | Zbl 0058.02202
Discrete Subgroups of Lie groups, Ergebnisse der Mathematik, 68, Springer-Verlag, Berlin, 1972. (1972) | MR 0507234
Some examples of symplectic manifolds, Proc. Amer. Math. Soc., 55 (1976), 467-468. (1976) | MR 0402764
Lectures on the Geometry of Poisson Manifolds, Progress in Math. 118, Birkhäuser, Basel, 1994. (1994) | MR 1269545 | Zbl 0810.53019
The local structure of Poisson manifolds, J. Differential Geometry 18 (1983), 523-557. Errata et addenda: J. Differential Geometry 22 (1985), 255. (1983) | MR 0723816 | Zbl 0524.58011