  The authors examine topological properties of the 7-dimensional Eschenburg
biquotients diag(z^k1,z^k2,z^k3)\SU(3)/diag(z^l1,z^l2,z^l3). A subfamily of
these spaces carry a 3-Sasakian metric. The authors show that among this
subfamily there exist many 3-Sasakian spaces which are homeomorphic but not
diffeomorphic. In addition, they construct a pair of 3-Sasakian spaces which
are diffeomorphic, thus giving the first example of a manifold which carries
two non-isometric 3-Sasakian metrics. This answers an open question of C. Boyer
and K.Galicki. Among the general family, the authors construct many pairs of
positively curved Eschenburg spaces which are homeomorphic but not
diffeomorphic. Such pairs were first constructed by Kreck-Stolz among the
special subfamily of Aloff-Wallach spaces.
