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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

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2021

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

    P 2/U(1)S 7 \mathbb{H}P^2 / \mathrm{U}(1) \simeq S^7 𝕆P 2/Sp(1)S 13 \mathbb{O}P^2 / \mathrm{Sp}(1) \simeq S^{13}

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 13th 2021
    • (edited Nov 13th 2021)

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

    P 1S 1;P 2/ConjS 4;(P 4/Aut())/ConjS 13.\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.