Geodesic
Minimal Euler characteristics for even-dimensional manifolds with finite fundamental group
Forum of Mathematics, Sigma, Tome 11 (2023)

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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 of type $F_n$. We define $q_{2n}(G)$, a generalised version of the Hausmann-Weinberger invariant [19] for 4–manifolds, as the minimal value of $(-1)^n\chi (M)$. For all $n\geq 2$, 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 nonabelian finite groups arising as fundamental groups of rational homology 4–spheres. 
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     author = {Alejandro Adem and Ian Hambleton},
     title = {Minimal {Euler} characteristics for even-dimensional manifolds with finite fundamental group},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.18},
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Alejandro Adem; Ian Hambleton. Minimal Euler characteristics for even-dimensional manifolds with finite fundamental group. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.18

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