ON THE J-ANTI-INVARIANT COHOMOLOGY OF ALMOST COMPLEX 4-MANIFOLDS

Abstract

For a compact almost complex 4-manifold (M, J), we study the subgroups H±J of H2(M, ℝ) consisting of cohomology classes representable by J-invariant, respectively, J-anti-invariant real 2-forms. If b+=1, we show that, for generic almost complex structures on M, the subgroup H−J is trivial. Computations of the subgroups and their dimensions h±J are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for h±J.