On a high-dimensional generalization of Seifert fibrations

The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto ${\mathbb C} P^2$ define such fibrations, and for them the characteristic classes corresponding to the generators of $H^2(B(U(2)/{\mathbb Z}_{2n});{\mathbb Z})$ are defined.