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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Obstruction formulas and almost-complex manifolds

Author: Robert D. Little
Journal: Proc. Amer. Math. Soc. 50 (1975), 459-462
MSC: Primary 57D25; Secondary 53C15
MathSciNet review: 0391116
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Abstract: 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.

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Keywords: Almost-complex manifolds, obstructions, lifting problems, vector fields, complex span
Article copyright: © Copyright 1975 American Mathematical Society

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