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Title: Poincaré duality complexes in dimension four
Contributor(s): Baues, Hans Joachim (author); Bleile, Beatrice  (author)
Publication Date: 2008
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Abstract: We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD⁴-complexes. Generalizing Turaev's fundamental triples of PD³-complexes we introduce fundamental triples of PDⁿ-complexes and show that two PDⁿ complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional manifolds.
Publication Type: Journal Article
Source of Publication: Algebraic and Geometric Topology, v.8, p. 2355-2389
Publisher: University of Warwick
Place of Publication: Warwick
ISSN: 1472-2747
Field of Research (FOR): 010112 Topology
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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