# Homotopy classification of $$\textit{PD}_4$$ PD 4 -complexes relative an order relation Academic Article

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### abstract

• 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.

• June 2015