nLab 13-sphere

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):

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

(Atiyah-Berndt 02)

References

• Michael Atiyah, Jürgen Berndt, in: Surv. Differ. Geom. VIII, Papers in Honor of Calabi, Lawson, Siu and Uhlenbeck (International Press, Somerville, MA, 2003) 1-27 (arXiv:math/0206135, doi:10.4310/SDG.2003.v8.n1.a1)