On cohomology of almost complex 4-manifolds
  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 and symplectic 2-form compatible almost complex structures. We prove that h_J = 0 for generic almost complex structures J on M. 
Qiang Tan, Hongyu Wang, Ying Zhang, and Peng Zhu
math.SG math.DG