Unit sphere fibrations in Euclidean space

Fuente: arXiv
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Autori principali: Asimov, Daniel, Frick, Florian, Harrison, Michael, Pegden, Wesley
Natura: Preprint
Pubblicazione: 2022
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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