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A REMARK ON THE STABLE REAL FORMS OF COMPLEX VECTOR BUNDLES OVER MANIFOLDS

Published online by Cambridge University Press:  13 March 2017

HUIJUN YANG*
Affiliation:
School of Mathematics and Statistics, Henan University, Kaifeng 475004, Henan, China email yhj@amss.ac.cn
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Abstract

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Let $M$ be an $n$-dimensional closed oriented smooth manifold with $n\equiv 4\;\text{mod}\;8$, and $\unicode[STIX]{x1D702}$ be a complex vector bundle over $M$. We determine the final obstruction for $\unicode[STIX]{x1D702}$ to admit a stable real form in terms of the characteristic classes of $M$ and $\unicode[STIX]{x1D702}$. As an application, we obtain the criteria to determine which complex vector bundles over a simply connected four-dimensional manifold admit a stable real form.

Type
Research Article
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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