The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929399694098432 |
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| author | Guerra, Lorenzo Jana, Santanil Maiti, Arun |
| author_facet | Guerra, Lorenzo Jana, Santanil Maiti, Arun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12990 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases Guerra, Lorenzo Jana, Santanil Maiti, Arun Algebraic Topology Functional Analysis 55R20, 20J06, 46B20, 52A20, 55M30 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. |
| title | The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases |
| topic | Algebraic Topology Functional Analysis 55R20, 20J06, 46B20, 52A20, 55M30 |
| url | https://arxiv.org/abs/2304.12990 |