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|Title:||Poincaré duality complexes in dimension four||Contributor(s):||Baues, Hans Joachim (author); Bleile, Beatrice (author)||Publication Date:||2008||Handle Link:||https://hdl.handle.net/1959.11/3032||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||Other Links:||www.mpim-bonn.mpg.de/preprints/send?bid=3558||Statistics to Oct 2018:||Visitors: 272
|Appears in Collections:||Journal Article|
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