Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincare Duality Pairs in Dimension Three   We extend Hendriks' classification theorem and Turaev's realisation and
splitting theorems for Poincare duality complexes in dimension three to the
relative case of Poincare duality pairs. The results for Poincare duality
complexes are recovered by restricting the results to the case of Poincare
duality pairs with empty boundary. Up to oriented homotopy equivalence,
three-dimensional Poincare duality pairs are classified by their fundamental
triple consisting of the fundamental group system, the orientation character
and the image of the fundamental class under the classifying map. Using the
derived module category we provide necessary and sufficient conditions for a
given triple to be realised by a three-dimensional Poincare duality pair. The
results on classification and realisation yield splitting or decomposition
theorems for three-dimensional Poincare duality pairs, that is, conditions
under which a given three-dimensional Poincare duality pair decomposes as
interior or boundary connected sum of two three-dimensional Poincare duality
pairs.

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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex