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 HJ is trivial. Computations of the subgroups and their dimensions h±J are obtained foralmost complex structures related to integrable ones. We also prove semi-continuity propertiesfor h±J.
Bibliographical noteFunding Information:
During the preparation of this work, the authors benefited from partial support from NSF grant DMS-0604748 (of the second author).