  Let P be a closed smooth (4j-2)-connected 8j-manifold. We complete Wilkens'
classification of the manifolds P for j = 1,2 and give an alternative proof to
Wall's classification of the manifolds for j > 2. The Hopf-invariant-one
dimensions (j=1,2) are characteristed by the fact that the quadratic linking
functions which classify may be inhomogeneous. Hence we also extend the
classification of (homogeneous) quadratic linking forms on finite abelian
groups (due to Nikulin) to the inhomogeneous case.
