Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collapsing 4-manifolds under a lower curvature bound   In this paper we describe the topology of 4-dimensional closed orientable
Riemannian manifolds with a uniform lower bound of sectional curvature and with
a uniform upper bound of diameter which collapse to metric spaces of lower
dimensions. This enables us to understand the set of homeomorphism classes of
closed orientable 4-manifolds with those geometric bounds on curvature and
diameter. In the course of the proof of the above results, we obtain the soul
theorem for 4-dimensional complete noncompact Alexandrov spaces with
nonnegative curvature. A metric classification for 3-dimensional complete
Alexandrov spaces with nonnegative curvature is also given.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph