Poincaré duality complexes in dimension four

Title
Poincaré duality complexes in dimension four
Publication Date
2008
Author(s)
Baues, Hans Joachim
Bleile, Beatrice
( author )
OrcID: https://orcid.org/0000-0003-2254-6832
Email: bbleile@une.edu.au
UNE Id une-id:bbleile
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Mathematical Sciences Publishers
Place of publication
United States of America
DOI
10.2140/agt.2008.8.2355
UNE publication id
une:3113
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.
Link
Citation
Algebraic & Geometric Topology, v.8, p. 2355-2389
ISSN
1472-2739
1472-2747
Start page
2355
End page
2389

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