Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915511560830976 |
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| author | Macías-Virgós, Enrique Tanré, Daniel |
| author_facet | Macías-Virgós, Enrique Tanré, Daniel |
| contents | Let $Q_n$ be the quasi-projective subspace of the symplectic group $\mathrm{Sp}(n)$. In this short note, we prove that the subspace Lusternik-Schnirelmann category of $Q_n$ in $\mathrm{Sp}(n)$ is 2. For that, we use a quaternionic logarithm, as Singhof did in the complex case for the determination of the Lusternik-Schnirelmann category of the unitary group.
Our result generalizes the known case $n=2$ (by L. Fernández-Suárez, A. Gómez-Tato and D. Tanré) and has to be compared to the equality $\mathrm{cat}\,Q_{3}=3$, established by N. Iwase and T. Miyauchi. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_20210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces Macías-Virgós, Enrique Tanré, Daniel Algebraic Topology 55M30, 57S15, 15B33, 57T10 Let $Q_n$ be the quasi-projective subspace of the symplectic group $\mathrm{Sp}(n)$. In this short note, we prove that the subspace Lusternik-Schnirelmann category of $Q_n$ in $\mathrm{Sp}(n)$ is 2. For that, we use a quaternionic logarithm, as Singhof did in the complex case for the determination of the Lusternik-Schnirelmann category of the unitary group. Our result generalizes the known case $n=2$ (by L. Fernández-Suárez, A. Gómez-Tato and D. Tanré) and has to be compared to the equality $\mathrm{cat}\,Q_{3}=3$, established by N. Iwase and T. Miyauchi. |
| title | Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces |
| topic | Algebraic Topology 55M30, 57S15, 15B33, 57T10 |
| url | https://arxiv.org/abs/2509.20210 |