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The Lefschetz property, formality and blowing up in symplectic geometry
Author(s):
Gil
Ramos
Cavalcanti
Journal:
Trans. Amer. Math. Soc.
359
(2007),
333-348.
MSC (2000):
Primary 53D35;
Secondary 57R19
Posted:
August 15, 2006
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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:
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
Posted:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Gil R. Cavalcanti, Formality of k-connected spaces in 4k+3- and 4k+4-dimensions, Math. Proc. Camb. Phil. Soc. 141 (2006), 101--112. (English)
Gil R. Cavalcanti, The decomposition of forms and cohomology of generalized complex manifolds, Journal of Geometry and Physics 57 (2007), 121 -- 132. (English)
M. Fernández; V. Muñoz; L. Ugarte , Weakly Lefschetz symplectic manifolds, Transactions of the American Mathematical Society 359 (2007), 851-1873. (english)
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