If n = 2, the Eells–Kuiper manifold is diffeomorphic to the real projective plane . For it is simply-connected and has the integral cohomology structure of the complex projective plane (), of the quaternionic projective plane () or of the Cayley projective plane (n = 16).
Theorem: Let be a connected closed manifold (not necessarily orientable) of dimension . Suppose admits a Morse function of class with exactly three singular points. Then is a Eells–Kuiper manifold.
- , and is homeomorphic to the sphere ,
- , and is an Eells—Kuiper manifold, or .
- Eells, James, Jr.; Kuiper, Nicolaas H. (1962), "Manifolds which are like projective planes", Institut des Hautes Études Scientifiques Publications Mathématiques (14): 5–46, MR 0145544.
- Camacho, César; Scárdua, Bruno (2008), "On foliations with Morse singularities", Proceedings of the American Mathematical Society, 136 (11): 4065–4073, MR 2425748, arXiv: , doi:10.1090/S0002-9939-08-09371-4.
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