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2008 Poincaré duality complexes in dimension four
Hans Joachim Baues, Beatrice Bleile
Algebr. Geom. Topol. 8(4): 2355-2389 (2008). DOI: 10.2140/agt.2008.8.2355

Abstract

Generalising Hendriks’ fundamental triples of PD3–complexes, we introduce fundamental triples for 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. Another main result describes chain complexes with additional algebraic structure which classify homotopy types of PD4–complexes. Up to 2–torsion, homotopy types of PD4–complexes are classified by homotopy types of chain complexes with a homotopy commutative diagonal.

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Hans Joachim Baues. Beatrice Bleile. "Poincaré duality complexes in dimension four." Algebr. Geom. Topol. 8 (4) 2355 - 2389, 2008. https://doi.org/10.2140/agt.2008.8.2355

Information

Received: 26 February 2008; Revised: 20 October 2008; Accepted: 26 October 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1164.57008
MathSciNet: MR2465744
Digital Object Identifier: 10.2140/agt.2008.8.2355

Subjects:
Primary: 57P10
Secondary: 55S35, 55S45

Rights: Copyright © 2008 Mathematical Sciences Publishers

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