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Abstract Brylinski introduced the symplectic analogue of harmonic forms on symplectic manifolds, thereby defining the symplectically harmonic cohomology space of a symplectic manifold. In this paper, we derive a formula for determining the sym-plectically harmonic Betti numbers of an arbitrary symplectic manifold of finite type, based on the dimensions of the kernels of the Lefschetz homomorphisms. Utilizing this formula, we compute the symplectically harmonic Betti numbers of a specific class of 4-dimensional symplectic manifolds, namely, McMullen-Taubes symplectic 4-manifolds, which includes the Kodaira-Thurston symplectic nilmanifold as a special case. MSC Classification: 53D05 , 53D35 , 57R17 , 57K43
Bynnud et al. (Tue,) studied this question.
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