The Lefschetz property, formality and blowing up in symplectic geometry

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...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2007-01, Vol.359 (1), p.333-348
Main Author: Cavalcanti, Gil Ramos
Format: Article
Language:English
Subjects:
Algebra
Differential geometry
Differential topology
Exact sciences and technology
Geometry
Lie groups
Manifolds and cell complexes
Mathematical manifolds
Mathematical theorems
Mathematics
Plant spines
Property titles
Riemann manifold
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-06-04058-X