The notion of projective space over the octonions makes sense for (but not beyond, see e.g. Voelkel 16, Sec. 1.3). The octonionic projective plane is also called the Cayley projective plane.
There is a homeomorphism
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.
The homotopy groups of octonionic projective plane are
Further homotopy groups are
(While , which includes the homotopy class of the octonionic Hopf fibration.)
For Ab any abelian group, then the ordinary cohomology groups of octionionic projective plane with coefficients in are
Malte Lackmann, The octonionic projective plane, in MATRIX Book Series 4, Springer (2021) [doi:10.1007/978-3-030-62497-2_6, arXiv:1909.07047]
Konrad Voelkel, Motivic cell structures for projective spaces over split quaternions, 2016 [freidok:11448, pdf]
Rowena Held, Iva Stavrov, Brian VanKoten, (Semi-)Riemannian geometry of (para-)octonionic projective planes, Diff. Geom. & its Appl. 27 4 (2009) 464-481 [doi:/10.1016/j.difgeo.2009.01.007]
Mamoru Mimura, The Homotopy groups of Lie groups of low rank, J. Math. Kyoto Univ. 6 2 (1967) 131-176 [doi:10.1215/kjm/1250524375]
Last revised on February 3, 2024 at 02:36:20. See the history of this page for a list of all contributions to it.