Minimal Euler Characteristics for Even-Dimensional Manifolds with Finite Fundamental Group

Abstract

We consider the Euler characteristics χ(M ) of closed orientable topological 2n-manifolds with (n−1)-connected universal cover and a given fundamental group G of type F n . We define q 2n (G), a generalized version of the Hausmann-Weinberger invariant [19] for 4-manifolds, as the minimal value of (−1) n χ(M ). For all n ≥ 2, we establish a strengthened and extended version of their estimates, in terms of explicit cohomological invariants of G. As an application we obtain new restrictions for non-abelian finite groups arising as fundamental groups of rational homology 4-spheres.