Diffeomorphism type of the Berger space

Abstract

We compute the Eells-Kuiper invariant of the Berger manifold SO(5)/SO(3) and determine that it is diffeomorphic to the total space of an S^3-bundle over S^4. This answers a question raised by K. Grove and W. Ziller.

LaTeX, 17 pages. v2: proofs of corollaries added

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