Diffeomorphism type of the Berger space
  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. 
Sebastian Goette, Nitu Kitchloo and Krishnan Shankar