Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal fibrations over noncommutative spheres   We present examples of noncommutative four-spheres that are base spaces of
$SU(2)$-principal bundles with noncommutative seven-spheres as total spaces.
The noncommutative coordinate algebras of the four-spheres are generated by the
entries of a projection which is invariant under the action of $SU(2)$. We give
conditions for the components of the Connes--Chern character of the projection
to vanish but the second (the top) one. The latter is then a non zero
Hochschild cycle that plays the role of the volume form for the noncommutative
four-spheres.

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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int