Eells–Kuiper manifold

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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