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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the divisibility of certain Chern numbers


Authors: Leonidas Charitos and Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 84 (1982), 272-274
MSC: Primary 57R20; Secondary 57R95
MathSciNet review: 637182
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Abstract: If $ M$ is a weakly almost complex manifold, then $ {c_r}(M) \in {H^{24}}(M;Z)$ is the $ r$th Chern class of its normal bundle.

Theorem 1. If $ m$, $ r$ are natural numbers with $ r \leqslant m$, then there exists a $ 2m$-fold $ {M_0}$, compact, closed and weakly almost complex, so that the normal characteristic number $ \left\langle {{c_r}({M_0}){c_{m - r}}({M_0})} \right.$, $ \left. {[{M_0}]} \right\rangle $ is a power of 2.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637182-1
PII: S 0002-9939(1982)0637182-1
Keywords: Characteristic number, Hattori-Stong Theorem
Article copyright: © Copyright 1982 American Mathematical Society