Unit sphere fibrations in Euclidean space

Abstract

We show that if an open set in ${\mathbb{R}}^d$ can be fibered by unit $n$-spheres, then $d\ge 2n+1$, 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 ${\mathbb{R}}^{2n+1}$.

11 pages, 3 figures

References in corpus (2)

• Contact structures induced by skew fibrations of R^3
• Circle Decompositions of Surfaces