octonionic projective space

The notion of projective space $\mathbb{O}P^n$ over the octonions $\mathbb{O}$ makes sense for $n \,\in\, \{ 0,1,2 \}$ (but not beyond, see e.g. Voelkel 16, Sec. 1.3).

We have a homeomorphism

$\mathbb{O}P^1 \,\simeq\, S^8$

between the octonionic projective line and the 8-sphere.

There is a homeomorphism

$\mathbb{O}P^2 \,\simeq\, S^{15} \underset{h_{\mathbb{O}}}{\cup} \mathbb{O}P^1$

between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.

See also at *cell structure of projective spaces*.

- Malte Lackmann,
*The octonionic projective plane*(arXiv:1909.07047)

See also

- Konrad Voelkel,
*Motivic cell structures for projective spaces over split quaternions*, 2016 (freidok:11448, pdf)

Last revised on December 17, 2020 at 04:29:17. See the history of this page for a list of all contributions to it.