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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Symplectic real Bott manifolds


Author: Hiroaki Ishida
Journal: Proc. Amer. Math. Soc. 139 (2011), 3009-3014
MSC (2010): Primary 57R17, 57S25
Published electronically: January 13, 2011
MathSciNet review: 2801640
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Abstract: A real Bott manifold is the total space of an iterated $ \mathbb{R}P^1$-bundle over a point, where each $ \mathbb{R}P^1$-bundle is the projectivization of a Whitney sum of two real line bundles. In this paper, we characterize real Bott manifolds which admit a symplectic form. In particular, it turns out that a real Bott manifold admits a symplectic form if and only if it is cohomologically symplectic. In this case, it admits even a Kähler structure. We also prove that any symplectic cohomology class of a real Bott manifold can be represented by a symplectic form. Finally, we study the flux of a symplectic real Bott manifold.


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Hiroaki Ishida
Affiliation: Graduate School of Science, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Email: hiroaki.ishida86@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10729-9
PII: S 0002-9939(2011)10729-9
Keywords: Toric topology, symplectic topology, real Bott manifold
Received by editor(s): January 19, 2010
Received by editor(s) in revised form: July 29, 2010
Published electronically: January 13, 2011
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.