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starting something, for the moment just so as to record that
there is a homeomorphism
between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.
finally realized that we already have Cayley plane. Have added cross-links now.
Hmm, is that meant to be ?
Yes, I changed it already on the page itself.
Added homotopy groups and cohomology of octonionic projective plane, already stated in Lackman 19 (https://arxiv.org/abs/1909.07047) already present on the page, and also in Mimura 67 (https://doi.org/10.1215/kjm/1250524375) now added as a new reference as well. Replaced 15-sphere by 16-disk in Proposition 2.2. as stated by both of those sources. (The same edit was done on Cayley plane.)
Something that I tried to highlight here is that these algebras coming from the Cayley-Dickson process are perhaps better understood not as “algebras lacking properties” but as “algebras with weakened properties”. Would it be possible then that the higher dimensional octonionic spaces do not have a manifold description but do admit a stacky presentation?
Hi Alonso, we had talked about this in another thread (here): Is it actually the case?
It’d be interesting if it were, but do you have an actual example?
I’m hoping to look into this when I get some time, but still wanted to pose the question in case there was already some work in this direction (the stacky character of projective spaces).
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