Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simply connected Alexandrov 4-manifolds with positive or nonnegative
  curvature and torus actions   We point out that a 4-dimensional topological manifold with an Alexandrov
metric (of curvature bounded below) and with an effective, isometric action of
the circle or the 2-torus is locally smooth. This observation implies that the
topological and equivariant classifications of compact, simply connected
Riemannian 4-manifolds with positive or nonnegative sectional curvature and an
effective isometric action of a circle or a 2-torus also hold if we consider
Alexandrov manifolds instead of Riemannian manifolds.

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th