2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132484We 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 addedDifferential GeometryAlgebraic Topology57R20 (primary); 53C30, 57S25, 55R25 (secondary)text