Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducibility of low dimensional Poincar\'e duality spaces   We discuss Poincar\'e duality complexes X and the question whether or not
their Spivak normal fibration admits a reduction to a vector bundle in the case
where the dimension of X is at most 4. We show that in dimensions less than 4
such a reduction always exists, and in dimension 4 such a reduction exists
provided X is orientable. In the non-orientable case there are counterexamples
to reducibility by Hambleton--Milgram.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg