Hodge structure on symplectic manifolds (Q1921270)
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scientific article; zbMATH DE number 915230
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hodge structure on symplectic manifolds |
scientific article; zbMATH DE number 915230 |
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Hodge structure on symplectic manifolds (English)
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23 September 1997
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The article deals with symplectic harmonic forms. A recent result by O. Mathieu states: For a symplectic manifold of \(\dim 2n\) the following properties are equivalent: (1) There exists a harmonic cocycle in every cohomology class and (2) the cup product is surjective. This article provides an alternative, more direct proof for this fact using a particular \(\text{sl}(2,C)\) representation. An application in symplectic differential topology concludes the paper.
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symplectic harmonic forms
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symplectic de Rham theory
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