  We study the topology of the 13 dimensional positively curved Bazaikin
spaces. We show that there is only one such manifold which is homotopy
equivalent to a homogeneous space, the so called Berger space. This is in
contrast to the case of the 7 dimensional positively curved Eschenburg spaces.
In addition, we compute the Pontryagin classes and the linking form and show
that the first two billion positively curved Bazaikin manifolds are
homeomorphically distinct, raising the question whether this is true in
general.
