The dδ–lemma for weakly Lefschetz symplectic manifold

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Mathematical Institute of Charles University in Prague
Google Scholar
Research Projects
Organizational Units
Journal Issue
For a symplectic manifold (M, ω), not necessarily hard Lefschetz, we prove a version of the Merkulov dδ–lemma ([17, 4]). We also study the dδ–lemma and related cohomologies for compact symplectic solvmanifolds.
9TH International Conference on Differential Geometry and its Applications.
UCM subjects
Unesco subjects
C. Benson and C.S. Gordon, Kahler and symplectic structures on nilmanifolds, Topology 27 (1988),513–518. J.L. Brylinski, A differential complex for Poisson manifolds, J. Diff. Geom. 28 (1988), 93–114. G.R. Cavalcanti, The Lefschetz property, formality and blowing up in symplectic geometry, Preprint math.SG/0403067. G.R. Cavalcanti, New aspects of the ddc-lemma, Ph. D.Thesis, University of Oxford, 2004. M. Fern´andez, M. de Leon and M. Saralegui, A six dimensional compact symplectic solvmanifold without Kahler structures, Osaka J. Math. 33 (1996), 19–35. M. Fernandez and V. Muñoz, Formality of Donaldson submanifolds, Math. Zeit., To appear. M. Fernandez, V. Muñoz and L. Ugarte, Weakly Lefschetz symplectic manifolds, Preprint math.SG/0404479. V. Guillemin, Symplectic Hodge theory and the dδ–lemma, Preprint, Massachusets Institute of Technology, 2001. A. Hattori, Spectral sequence in the de Rham cohomology of fibre bundles, J. Fac. Sci. Univ. Tokyo 8 (1960), 298–331. R. Ibañez, Y. Rudyak, A. Tralle and L. Ugarte, On symplectically harmonic forms on 6–dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), 89–109. J.L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, in Elie Cartan et les Math. d’Aujour d’Hui, Asterisque hors-serie (1985), 251–271. P. Libermann, Sur le probleme d’equivalence de certaines structures infinitesimales regulieres, Ann.Mat. Pura Appl. 36 (1954), 27–120. P. Libermann and C. Marle, Symplectic Geometry and Analytical Mechanics, Kluwer, Dordrecht,1987. A. Lichnerowicz, Les varietes de Poisson et les algebres de Lie associees, J. Diff. Geom. 12 (1977),253–300. Y. Lin and R. Sjamaar, Equivariant symplectic Hodge theory and the dGδ–lemma, J. Symplectic Geom., To appear, Preprint math.SG/0310048. O.Mathieu, Harmonic cohomology classes of symplectic manifolds, Comment. Math. Helv. 70 (1995),1–9. S. Merkulov, Formality of canonical symplectic complexes and Frobenius manifolds, Internat. Math.Res. Notices 14 (1998), 723–733. K. Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. 59 (1954), 531-538. W.P. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976),467–468. R.Wells, Differential analysis on complex manifolds. Second edition. Graduate Texts in Mathematics 65. Springer-Verlag, New York-Berlin, 1980. T. Yamada, Harmonic cohomology groups of compact symplectic nilmanifolds, Osaka J. Math. 39 (2002), 363–381. D. Yan, Hodge structure on symplectic manifolds, Adv. Math. 120 (1996), 143–154.