Unit sphere fibrations in Euclidean space
| Autor: | Asimov, Daniel, Frick, Florian, Harrison, Michael, Pegden, Wesley |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the Edinburgh Mathematical Society 67 (2024) 287-298 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0013091524000038 |
| Popis: | We show that if an open set in $\mathbb{R}^d$ can be fibered by unit $n$-spheres, then $d \geq 2n+1$, and if $d = 2n+1$, then the spheres must be pairwise linked, and $n \in \left\{ 0, 1, 3, 7 \right\}$. For these values of $n$, we construct unit $n$-sphere fibrations in $\mathbb{R}^{2n+1}$. Comment: 11 pages, 3 figures |
| Databáze: | arXiv |
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