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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Lefschetz property, formality and blowing up in symplectic geometry


Author: Gil Ramos Cavalcanti
Journal: Trans. Amer. Math. Soc. 359 (2007), 333-348
MSC (2000): Primary 53D35; Secondary 57R19
Published electronically: August 15, 2006
MathSciNet review: 2247894
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Abstract: In this paper we study the behaviour of the Lefschetz property under the blow-up construction. We show that it is possible to reduce the dimension of the kernel of the Lefschetz map if we blow up along a suitable submanifold satisfying the Lefschetz property. We use this, together with results about Massey products, to construct compact nonformal symplectic manifolds satisfying the Lefschetz property.


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Additional Information

Gil Ramos Cavalcanti
Affiliation: Mathematical Institute, University of Oxford, St. Giles 24-29, Oxford, OX1 3BN, United Kingdom
Email: gilrc@maths.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04058-X
PII: S 0002-9947(06)04058-X
Keywords: Strong Lefschetz property, symplectic blow-up, Massey products
Received by editor(s): November 14, 2004
Published electronically: August 15, 2006
Additional Notes: This research was supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Ministério da Educação e Cultura), Brazilian Government, Grant 1326/99-6
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.