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1 results

Unit sphere fibrations in Euclidean space
Part of
- Differential topology
- Fiber spaces and bundles
Daniel Asimov, Florian Frick, Michael Harrison, Wesley Pegden
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 2 / May 2024

Published online by Cambridge University Press:

07 March 2024, pp. 287-298
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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 $\mathbb{R}^{2n+1}$.