No CrossRef data available.
Article contents
Unit sphere fibrations in Euclidean space
Published online by Cambridge University Press: 07 March 2024
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
$\mathbb{R}^{2n+1}$.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline167.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline168.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline169.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline170.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline171.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline172.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline173.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline174.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240515113554835-0226:S0013091524000038:S0013091524000038_inline175.png?pub-status=live)