Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse-Novikov cohomology of locally conformally K\"ahler surfaces   We review the properties of the Morse-Novikov cohomology and compute it for
all known compact complex surfaces with locally conformally K\"ahler metrics.
We present explicit computations for the Inoue surfaces $\mathcal{S}^0$,
$\mathcal{S}^+$, $\mathcal{S}^-$ and classify the locally conformally K\"ahler
(and the tamed locally conformally symplectic) forms on $\mathcal{S}^0$. We
prove the nonexistence of LCK metrics with potential and more generally, of
$d_\theta$-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex