Unit sphere fibrations in Euclidean space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909207380361216 |
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| author | Asimov, Daniel Frick, Florian Harrison, Michael Pegden, Wesley |
| author_facet | Asimov, Daniel Frick, Florian Harrison, Michael Pegden, Wesley |
| contents | 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 $\mathbb{R}^{2n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13981 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Unit sphere fibrations in Euclidean space Asimov, Daniel Frick, Florian Harrison, Michael Pegden, Wesley Geometric Topology 55R25, 57R22, 57R30 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 $\mathbb{R}^{2n+1}$. |
| title | Unit sphere fibrations in Euclidean space |
| topic | Geometric Topology 55R25, 57R22, 57R30 |
| url | https://arxiv.org/abs/2210.13981 |