On the minimal sum of Betti numbers of an almost complex manifold

2018/05/12 by Albanese, Michael, Milivojevic, Aleksandar
#32Q60 #53C15 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.04751

Abstract

We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.

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