Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to nonnegative curvature and rational homotopy theory   We establish a link between rational homotopy theory and the problem which
vector bundles admit complete Riemannian metric of nonnegative sectional
curvature. As an application, we show for a large class of simply-connected
nonnegatively curved manifolds that, if C lies in the class and T is a torus of
positive dimension, then "most" vector bundles over the product of C and T
admit no complete nonnegatively curved metric.

32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex