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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0391116-2
PII: S 0002-9939(1975)0391116-2
Keywords: Almost-complex manifolds, obstructions, lifting problems, vector fields, complex span
Article copyright: © Copyright 1975 American Mathematical Society