Abstract
Based on recent work of T. Draghici, T.-J. Li, and W. Zhang, we further investigate properties of the dimension \(h_J^-\) of the \(J\)-anti-invariant cohomology subgroup \(H_J^-\) of a closed almost Hermitian 4-manifold \((M,g,J,F)\) using metric compatible almost complex structures. We prove that \(h_J^-=0\) for generic almost complex structures \(J\) on \(M\).
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