Obstruction Formulas and Almost-Complex Manifolds

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This paper contains three theorems about almost-complex manifolds. The first theorem states that, under certain conditions, the Euler characteristic of an almost-complex manifold ${M^{2n}}$ must be divisible by $(n - 1)!$. This theorem implies that if ${M^{2n}}$ is an almost-complex homology sphere, then $n \leq 3$. The next two theorems concern the maximal number of vector fields of an almost-complex manifold which are linearly independent over the complex numbers.