Unit sphere fibrations in Euclidean space

Abstract

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

Locations

• Proceedings of the Edinburgh Mathematical Society - View
• arXiv (Cornell University) - View - PDF