PD4-complexes with fundamental group a PD2-group

We show that if the fundamental group π of a PD4-complex X has cohomological dimension 2 there is a 2-connected degree 1 map from X to a “minimal” such complex. If moreover π has one end we relate the cohomological linking pairing to the attaching map for the top cell via the Whitehead quadratic functor, and show that every w-hermitian form on a finitely generated projective Z[π]-module is realized by some PD4-complex with fundamental group π. If π is a PD2-group the minimal complex is the total space of an S2-bundle over K(π,1) and is determined by cohomological invariants of X.