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The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases
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abstract
Unordered flag manifolds are the manifolds of unordered $n$-tuple of mutually orthogonal lines in $\mathbb{R}^n$. In this paper, we develop some basic tools to compute the mod-$2$ cohomology groups of these spaces, and apply them for explicit computation for small $n$. We show that this computation improves the known estimate of the number of Auerbach bases of normed linear spaces of small dimensions.
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