  We compute the topological simple structure set of closed manifolds which
occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an
n-dimensjional torus T^n for an odd prime p and l greater or equal to 3,
provided that the induced Z/p-action on pi_1(T^n) = Z^n is free outside the
origin. To the best of our knowledge this is the first computation of the
structure set of a topological manifold whose fundamental group is not obtained
from torsionfree and finite groups using amalgamated and HNN-extensions. We
give a collection of classical surgery invariants such as splitting
obstructions and rho-invariants which decide whether a simple homotopy
equivalence from a closed topological manifold to M is homotopic to a
homeomorphism.
