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Coeffective cohomology of symplectic aspherical manifolds. (English) Zbl 1277.53081
A differential form \(\alpha\) on a compact symplectic manifold \((M,\omega)\) is coeffective if \(\alpha\wedge\omega=0\). The coeffective cohomology of \(M\) is the cohomology of the sub-DGA consisting of all coeffective forms on \(M\). On any compact Kähler manifold, the de Rham cohomology groups are isomorphic to the coeffective cohomology groups at higher degrees. However, this result does not hold for general symplectic manifolds. The author computes the coeffective cohomology of some class of symplectic manifolds, and gives non-Kähler symplectic manifolds which have also isomorphic coeffective cohomology and de Rham cohomology.
Reviewer: Hao Ding (Chengdu)

MSC:
53D05 Symplectic manifolds, general
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