Maps from Grassmannians of 2-planes to projective spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915117889748992 |
|---|---|
| author | Brasil, Ricardo Ferreira, Ana Cristina Vandembroucq, Lucile |
| author_facet | Brasil, Ricardo Ferreira, Ana Cristina Vandembroucq, Lucile |
| contents | Using quaternions and octonions, we construct some maps from the Grassmannian of 2-dimensional planes of $\mathbb{R}^n$, $\mathrm{Gr}_2(\mathbb{R}^n)$, to the projective space $\mathbb{R}\mathrm{P}^k$, for certain values of $n$ and $k$. All of our maps induce an isomorphism at the level of fundamental groups, and two of them are shown to be submersions. As an application, we obtain new estimates of the Lusternik-Schnirelmann category of $\mathrm{Gr}_2(\mathbb{R}^n)$ for specific values of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maps from Grassmannians of 2-planes to projective spaces Brasil, Ricardo Ferreira, Ana Cristina Vandembroucq, Lucile Algebraic Topology Geometric Topology 57R19, 57S25, 55M30, 53C30 Using quaternions and octonions, we construct some maps from the Grassmannian of 2-dimensional planes of $\mathbb{R}^n$, $\mathrm{Gr}_2(\mathbb{R}^n)$, to the projective space $\mathbb{R}\mathrm{P}^k$, for certain values of $n$ and $k$. All of our maps induce an isomorphism at the level of fundamental groups, and two of them are shown to be submersions. As an application, we obtain new estimates of the Lusternik-Schnirelmann category of $\mathrm{Gr}_2(\mathbb{R}^n)$ for specific values of $n$. |
| title | Maps from Grassmannians of 2-planes to projective spaces |
| topic | Algebraic Topology Geometric Topology 57R19, 57S25, 55M30, 53C30 |
| url | https://arxiv.org/abs/2501.13590 |