Real spin bundles over $\mathbb{C}\mathrm{P}^3$ and a new Euclidean embedding of $\mathbb{R}\mathrm{P}^7$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914159890792448 |
|---|---|
| author | Gdesz, Dominik |
| author_facet | Gdesz, Dominik |
| contents | We generalize the $α$-invariant introduced by Atiyah and Rees to an invariant of real spin bundles and use it to classify real bundles over $\mathbb{C}\mathrm{P}^3$ admitting spin structure. We apply this result to show that $\mathbb{R}\mathrm{P}^7$ can be smoothly embedded in $\mathbb{R}\mathrm{P}^{11}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real spin bundles over $\mathbb{C}\mathrm{P}^3$ and a new Euclidean embedding of $\mathbb{R}\mathrm{P}^7$ Gdesz, Dominik Algebraic Topology 57R40 (Primary) 55R25, 55R50 (Secondary) We generalize the $α$-invariant introduced by Atiyah and Rees to an invariant of real spin bundles and use it to classify real bundles over $\mathbb{C}\mathrm{P}^3$ admitting spin structure. We apply this result to show that $\mathbb{R}\mathrm{P}^7$ can be smoothly embedded in $\mathbb{R}\mathrm{P}^{11}$. |
| title | Real spin bundles over $\mathbb{C}\mathrm{P}^3$ and a new Euclidean embedding of $\mathbb{R}\mathrm{P}^7$ |
| topic | Algebraic Topology 57R40 (Primary) 55R25, 55R50 (Secondary) |
| url | https://arxiv.org/abs/2511.12172 |