Unit sphere fibrations in Euclidean space

Author:

Asimov Daniel,Frick FlorianORCID,Harrison MichaelORCID,Pegden Wesley

Abstract

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

Publisher

Cambridge University Press (CUP)

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