Symplectic manifolds and formality. (English) Zbl 0789.55010
The paper begins with the question: Is every 1-connected compact symplectic manifold a formal space? This question originates in the well known result of Deligne, Griffiths, Morgan and Sullivan: A compact 1- connected Kähler manifold is formal.
Using techniques of rational homotopy the authors assume the presence of a symplectic structure on a manifold and establish extra conditions (pure minimal model, coformal model) sufficient to imply formality.
In the second part of the paper they prove that a nilmanifold\(X\) with \(H^*(X,\mathbb{Q})\) a Lefschetz algebra is diffeomorphic to a torus.
Using techniques of rational homotopy the authors assume the presence of a symplectic structure on a manifold and establish extra conditions (pure minimal model, coformal model) sufficient to imply formality.
In the second part of the paper they prove that a nilmanifold\(X\) with \(H^*(X,\mathbb{Q})\) a Lefschetz algebra is diffeomorphic to a torus.
Reviewer: Y.Felix (Louvain-La-Neuve)
MSC:
| 55P62 | Rational homotopy theory |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
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