We consider 2 types of minimal Poincaré 4 -complexes. One is defined with respect to the degree 1 -map order. This idea was already present in our previous papers, and more systematically studied later by Hillman. The second type of minimal Poincaré 4 -complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.
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