Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $L_2$-cohomology of almost Hermitian manifolds   Let $(X,J,\omega,g)$ be a complete $n$-dimensional K\"ahler manifold. A
Theorem by Gromov \cite{G} states that the if the K\"ahler form is $d$-bounded,
then the space of harmonic $L_2$ forms of degree $k$ is trivial, unless
$k=\frac{n}{2}$. Starting with a contact manifold $(M,\alpha)$ we show that the
same conclusion does not hold in the category of almost K\"ahler manifolds. Let
$(X,J,g)$ be a complete almost Hermitian manifold of dimension four. We prove
that the reduced $L_2$ $2^{nd}$-cohomology group decomposes as direct sum of
the closure of the invariant and anti-invariant $L_2$-cohomology. This
generalizes a decomposition theorem by Dr\v{a}ghici, Li and Zhang \cite{DLZ}
for $4$-dimensional closed almost complex manifolds to the $L_2$-setting.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg