欧几里得空间中的单位球纤维

Pub Date : 2024-03-07 DOI:10.1017/s0013091524000038
Daniel Asimov, Florian Frick, Michael Harrison, Wesley Pegden
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引用次数: 0

摘要

我们证明,如果$\mathbb{R}^d$中的一个开集可以被单位n球纤维化,那么$d \geq 2n+1$,如果$d = 2n+1$,那么球体必须是成对链接的,并且$n \in \left\{0,1,3,7 \right\}$。对于这些 n 值,我们在 $\mathbb{R}^{2n+1}$ 中构造单位 n 球纤维。
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Unit sphere fibrations in Euclidean space

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 $\mathbb{R}^{2n+1}$.

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