On the minimal sum of Betti numbers of an almost complex manifold |
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Affiliation: | Stony Brook University, Department of Mathematics, United States of America |
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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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Keywords: | Almost complex manifolds Rational homology spheres Rational projective planes |
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