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

2021/03/01 by Adem, Alejandro, Hambleton, Ian
#20J06 #57S17 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2103.00703

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 for 4-manifolds, as the minimal value of (-1)ⁿχ(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.

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