2 results
The ER(z)-cohomology of Bℤ/(2q) and ℂℙn
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 191-217
- Print publication:
- 01 February 2018
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- Article
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- You have access
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The
$ER\left( 2 \right)$-cohomology of 
$B\mathbb{Z}/\left( {{2}^{q}} \right)$ and 
$\mathbb{C}{{\mathbb{P}}^{n}}$ are computed along with the Atiyah–Hirzebruch spectral sequence for 
$ER{{\left( 2 \right)}^{*}}\left( \mathbb{C}{{\mathbb{P}}^{\infty }} \right)$. This, along with other papers in this series, gives us the $ER\left( 2 \right)$-cohomology of all Eilenberg–MacLane spaces.
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.
