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Harmonic cohomology of symplectic fiber bundles


Authors: Oliver Ebner and Stefan Haller
Journal: Proc. Amer. Math. Soc. 139 (2011), 2927-2931
MSC (2010): Primary 53D17
Published electronically: December 28, 2010
MathSciNet review: 2801633
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Abstract: We show that every de Rham cohomology class on the total space of a symplectic fiber bundle with closed Lefschetz fibers admits a Poisson harmonic representative in the sense of Brylinski. The proof is based on a new characterization of closed Lefschetz manifolds.


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Additional Information

Oliver Ebner
Affiliation: Institute of Geometry, Technische Universität Graz, Kopernikusgasse 24/IV, A-8010 Graz, Austria
Email: o.ebner@tugraz.at

Stefan Haller
Affiliation: Department of Mathematics, University of Vienna, Nordbergstraße 15, A-1090, Vienna, Austria
Email: stefan.haller@univie.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10707-4
Keywords: Brylinski problem, Poisson manifolds, harmonic cohomology
Received by editor(s): April 13, 2010
Received by editor(s) in revised form: July 19, 2010
Published electronically: December 28, 2010
Additional Notes: The first author was partially supported by the Austrian Science Fund, grant S9209
The second author acknowledges the support of the Austrian Science Fund, grant P19392-N13.
Communicated by: Jianguo Cao
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.