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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 4th 2020
• (edited Aug 4th 2020)

this used to be inside 4-sphere. Am giving it its stand-alone entry for ease of listing references

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 6th 2021

I have added statement of and references for the generalizations of the theorem to quaternionic- and octonionic projective planes:

$\mathbb{H}P^2 / \mathrm{U}(1) \simeq S^7$ $\mathbb{O}P^2 / \mathrm{Sp}(1) \simeq S^{13}$
• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeNov 13th 2021
• (edited Nov 13th 2021)

I see Arnold in his article sets the $S^4$ result in a different series, in terms of a trinity

$\mathbb{R}P^1 \simeq S^1; \mathbb{C}P^2/Conj \simeq S^4; (\mathbb{H}P^4/Aut(\mathbb{H}))/Conj \simeq S^13.$