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

@article{Albanese2018OnTM,
  title={On the minimal sum of Betti numbers of an almost complex manifold.},
  author={Michael J. Albanese and Aleksandar Milivojevi{\'c}},
  journal={arXiv: Algebraic Topology},
  year={2018}
}
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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