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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 4th 2020
   • (edited Aug 4th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexthis used to be inside _[[4-sphere]]_. Am giving it its stand-alone entry for ease of listing references <a href="https://ncatlab.org/nlab/revision/Arnold-Kuiper-Massey+theorem/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Arnold-Kuiper-Massey+theorem">current</a>

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

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added statement of and references for the generalizations of the theorem to quaternionic- and octonionic projective planes: $$ \mathbb{H}P^2 / \mathrm{U}(1) \simeq S^7 $$ $$ \mathbb{O}P^2 / \mathrm{Sp}(1) \simeq S^{13} $$ <a href="https://ncatlab.org/nlab/revision/diff/Arnold-Kuiper-Massey+theorem/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/Arnold-Kuiper-Massey+theorem/4">v4</a>, <a href="https://ncatlab.org/nlab/show/Arnold-Kuiper-Massey+theorem">current</a>

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

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

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 13th 2021
   • (edited Nov 13th 2021)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI see Arnold in his [article](https://ncatlab.org/nlab/show/Arnold-Kuiper-Massey+theorem#Arnold99) sets the $S^4$ result in a different series, in terms of a trinity $$\mathbb{R}P^1 \simeq S^1; \mathbb{C}P^2/Conj \simeq S^4; (\mathbb{H}P^4/Aut(\mathbb{H}))/Conj \simeq S^13.$$

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

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