Abstract
We extend Hendriks' classification theorem and Turaev's realisation and splitting theorems for PD3-complexes to the relative case of PD3-pairs. The results for PD3-complexes are recovered by restricting the results to the case of PD3-pairs with empty boundary. Up to oriented homotopy equivalence, PD3-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 PD3-pair. The results on classification and realisation yield splitting or decomposition theorems for PD3-pairs, that is, conditions under which a given PD3-pair decomposes as interior or boundary connected sum of two PD3-pairs.
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