# nLab 13-sphere

Contents

### Context

#### Spheres

n-sphere

low dimensional n-spheres

# Contents

## Idea

The n-sphere of dimension $n = 13$.

## Properties

### AKM-Theorem

In higher-dimensional analogy to the AKM-theorem we have:

###### Proposition

The 13-sphere is the quotient space of the (right-)octonionic projective plane by the left multiplication action by Sp(1):

$\mathbb{O}P^2 / \mathrm{Sp}(1) \simeq S^{13}$

## References

Created on February 6, 2021 at 23:58:23. See the history of this page for a list of all contributions to it.