Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic torus bundles and group extensions   Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second
cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
ingredient is the notion of fibrewise-localization.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
20
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: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas