On the J-anti-invariant cohomology of almost complex 4-manifolds

Details On the J-anti-invariant cohomology of almost complex 4-manifolds On the J-anti-invariant cohomology of almost complex 4-manifolds

2011-04-13

arxiv.org/abs/1104.2511v1

Mathematics

Symplectic Geometry

30 pages

Scientific paper

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 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 $h^{\pm}_J$ are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for $h^{\pm}_J$.

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