In mathematics, an Eells–Kuiper manifold is a compactification of
by a sphere of dimension
It is named after James Eells and Nicolaas Kuiper.
, the Eells–Kuiper manifold is diffeomorphic to the real projective plane
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 (
These manifolds are important in both Morse theory and foliation theory: Theorem:[1] Let
be a connected closed manifold (not necessarily orientable) of dimension
admits a Morse function
be a compact connected manifold and
a Morse foliation on
Suppose the number of centers
is more than the number of saddles
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