Discussion of $\mathbb{Z}_2$-equivariant stable homotopy groups/equivariant stable cohomotopy of spheres:
Shôrô Araki, Kouyemon Iriye, Equivariant stable homotopy groups of spheres with involutions. I, Osaka J. Math. Volume 19, Number 1 (1982), 1-55. (Euclid:1200774828)
Kouyemon Iriye, Equivariant stable homotopy groups of spheres with involutions. II, Osaka J. Math. Volume 19, Number 4 (1982), 733-743 (euclid:1200775536)
On (among other things) coset space-realizationa of complex projective 3-space:
Discussion of fiberwise H-space-structure on spheres, quaternionic Hopf fibration, octonionic Hopf fibration, see also at Hopf construction):
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