Minimal Euler characteristics for even-dimensional manifolds with finite fundamental group

Abstract We consider the Euler characteristics $\chi (M)$ of closed, orientable, topological $2n$ -manifolds with $(n-1)$ -connected universal cover and a given fundamental group G type $F_n$ . define $q_{2n}(G)$ , generalised version Hausmann-Weinberger invariant [19] for 4–manifolds, as minimal value $(-1)^n\chi For all $n\geq 2$ we establish strengthened extended their estimates, in terms explicit cohomological invariants As an application, obtain new restrictions nonabelian finite groups arising rational homology 4–spheres.