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arXiv · 2304.12990

The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases

Lorenzo Guerra·Santanil Jana·Arun Maiti
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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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Lorenzo Guerra, Santanil Jana, Arun Maiti. 2023-04-25. The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases. https://arxiv.org/abs/2304.12990

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