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Homotopy classification of \(PD_4\)-complexes relative an order relation. (English) Zbl 1401.57032

Summary: We define an order relation among oriented \(PD_4\)-complexes. We show that with respect to this relation, two \(PD_4\)-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.

MSC:

57P10 Poincaré duality spaces
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
55S35 Obstruction theory in algebraic topology
55S45 Postnikov systems, \(k\)-invariants
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