# 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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