Embedding 4-manifolds with vanishing second homology

In this paper we study algebraic and geometric properties of closed oriented smooth 4-manifolds M with H2(M;Z)≅0. Moreover, we investigate the problem of embedding M in 5-space or other standard simply-connected 5-manifolds according to Bardenʹs list [Ann. of Math. 82 (1965) 365–385]. These results are related with papers [Invent. Math. 77 (1984) 173–184; Topology 23 (1984) 257–269] of Cochran.