Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective product spaces   Let nbar=(n_1,...,n_r). The quotient space P_nbar:=(S^{n_1} x...x S^{n_r})/(x
~ -x)is what we call a projective product space. We determine the integral
cohomology ring and the action of the Steenrod algebra. We give a splitting of
Sigma P_nbar in terms of stunted real projective spaces, and determine when
S^{n_i} is a product factor. We relate the immersion dimension and span of
P_nbar to the much-studied sectioning question for multiples of the Hopf bundle
over real projective spaces. We show that the immersion dimension of P_nbar
depends only on min(n_i), sum n_i, and r, and determine its precise value
unless all n_i exceed 9. We also determine exactly when P_nbar is
parallelizable.

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The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con