Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classification of 5-dimensional manifolds, souls of codimension two
  and non-diffeomorphic pairs   Let T(\gamma) be the total space of the canonical line bundle \gamma over
CP^1 and r an integer which is greater than one and coprime to six. We prove
that L_r^3\times T(\gamma) admits an infinite sequence of metrics of
nonnegative sectional curvature with pairwise non-homeomorphic souls, where
L_r^3 is the standard 3-dimensional lens space with fundamental group
isomorphic to Z/r. We classify the total spaces of S^1-fibre bundles over
S^2\times S^2 with fundamental group isomorphic to Z/r up to diffeomorphism and
use these results to give examples of manifolds N which admit two complete
metrics of nonnegative sectional curvature with souls S and S' of codimension
two such that S and S' are diffeomorphic whereas the pairs (N,S) and (N,S') are
not diffeomorphic. This solves a problem posed by I. Belegradek, S. Kwasik and
R. Schultz.

6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ