Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/7477
Title: Poincaré duality pairs of dimension three
Contributor(s): Bleile, Beatrice  (author)
Publication Date: 2010
DOI: 10.1515/FORUM.2010.016
Handle Link: https://hdl.handle.net/1959.11/7477
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.
Publication Type: Journal Article
Source of Publication: Forum Mathematicum, 22(2), p. 277-301
Publisher: Walter de Gruyter
Place of Publication: Germany
ISSN: 1435-5337
0933-7741
Field of Research (FOR): 010112 Topology
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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