Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the J-anti-invariant cohomology of almost complex 4-manifolds   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 $h^{\pm}_J$.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ