The index of equidimensional flag manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912347414593536 |
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| author | Basu, Samik Kundu, Bikramjit |
| author_facet | Basu, Samik Kundu, Bikramjit |
| contents | In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be thought of as an odd primary version of the computations of Baralić et al [Forum Math., 30 (2018), pp. 1539--1572] for the Grassmann manifold $G_n(\mathbb{R}^{2n})$. These results have geometric consequences for $p$-fold orthogonal shadows of a convex body. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13302 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The index of equidimensional flag manifolds Basu, Samik Kundu, Bikramjit Algebraic Topology Metric Geometry Primary: 55M20, 55M35, Secondary: 52A35, 55N91 In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be thought of as an odd primary version of the computations of Baralić et al [Forum Math., 30 (2018), pp. 1539--1572] for the Grassmann manifold $G_n(\mathbb{R}^{2n})$. These results have geometric consequences for $p$-fold orthogonal shadows of a convex body. |
| title | The index of equidimensional flag manifolds |
| topic | Algebraic Topology Metric Geometry Primary: 55M20, 55M35, Secondary: 52A35, 55N91 |
| url | https://arxiv.org/abs/2207.13302 |