\(PD_4\)-complexes with free fundamental group (Q1775304)

This paper gives purely homological proofs of results on the structure of Poincaré 4-complexes with free fundamental group. It is shown that such spaces are determined by their intersection pairings and that every hermitian form on a finitely generated free module over the group ring of a free group can be so realized. Once it is shown that the 3-skeleton is a wedge of spheres the results are obtained by computing with the chain groups. A final section considers the classification of 4-manifolds with free fundamental group up to \(s\)-cobordism.