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A REMARK ON THE STABLE REAL FORMS OF COMPLEX VECTOR BUNDLES OVER MANIFOLDS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 1 / August 2017
- Published online by Cambridge University Press:
- 13 March 2017, pp. 69-76
- Print publication:
- August 2017
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- Article
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- You have access
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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.
