Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvable models for Kodaira surfaces   We consider three families of lattices on the oscillator group $G$, which is
an almost nilpotent not completely solvable Lie group, giving rise to coverings
$G \to M_{k, 0} \to M_{k, \pi} \to M_{k, \pi/2}$ for $k\in \Z$. We show that
the corresponding families of four dimensional solvmanifolds are not pairwise
diffeomorphic and we compute their cohomology and minimal models. In
particular, each manifold $M_{k, 0}$ is diffeomorphic to a Kodaira--Thurston
manifold, i.e. a compact quotient $S^1 \times \Heis_3 (\R) /\Gamma_k$ where
$\Gamma_k$ is a lattice of the real three-dimensional Heisenberg group $\Heis_3
(\R)$. We summarize some geometric aspects of those compact spaces. In
particular, we note that any $M_{k, 0}$ provides an example of a solvmanifold
whose cohomology does not depend on the Lie algebra only and which admits many
symplectic structures that are invariant by the group $\R \times\Heis_3 (\R)$
but not under the oscillator group $G$.

20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph