Spin actions and Polygon spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914072680726528 |
|---|---|
| author | Lee, Eunjeong Lee, Jae-Hyouk |
| author_facet | Lee, Eunjeong Lee, Jae-Hyouk |
| contents | In this article, we construct correspondences between polygon spaces in Euclidean spaces of dimension $2,3,5,9\ $and the quotient spaces of $2$-Steifel manifolds along the normed division algebra$\ \mathbb{F}$ real $\mathbb{R}$, complex $\mathbb{C}$, quaternions $\mathbb{H}$, octonions $\mathbb{O}$. For the purpose, we introduce Hopf map on $\mathbb{F}^{2}\ $and consider the spin action of $SU\left( 2,\mathbb{F}\right) $ to spinor $\mathbb{F}^{2}\ $and the induced $SO\ $action to the Euclidean space $\mathbb{R\oplus F}$. The correspondences are extension of the work of Hausmann and Knutson for polygon spaces of dimension $2,3\ $and $2$-Grassmannians over real and complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spin actions and Polygon spaces Lee, Eunjeong Lee, Jae-Hyouk Differential Geometry 53C27, 53C30, 57T15, 57S25, 17A75 In this article, we construct correspondences between polygon spaces in Euclidean spaces of dimension $2,3,5,9\ $and the quotient spaces of $2$-Steifel manifolds along the normed division algebra$\ \mathbb{F}$ real $\mathbb{R}$, complex $\mathbb{C}$, quaternions $\mathbb{H}$, octonions $\mathbb{O}$. For the purpose, we introduce Hopf map on $\mathbb{F}^{2}\ $and consider the spin action of $SU\left( 2,\mathbb{F}\right) $ to spinor $\mathbb{F}^{2}\ $and the induced $SO\ $action to the Euclidean space $\mathbb{R\oplus F}$. The correspondences are extension of the work of Hausmann and Knutson for polygon spaces of dimension $2,3\ $and $2$-Grassmannians over real and complex. |
| title | Spin actions and Polygon spaces |
| topic | Differential Geometry 53C27, 53C30, 57T15, 57S25, 17A75 |
| url | https://arxiv.org/abs/2510.03067 |