Minimal 4-manifolds for groups of cohomological dimension 2

Abstract

We show that if π is a group with a finite 2-dimensional Eilenberg-Mac Lane complex then the minimum of the Euler characteristics of closed 4-manifolds with fundamental group π is 2χ(K(π, 1)). If moreoverMis such a manifold realizing this minimum then π2(M) ≅Similarly, if π is a PD3-group andw1(M) is the canonical orientation character of π then χ(M)≧l and π2(M) is stably isomorphic to the augmentation ideal ofZ[π].