  Given a map f: M \to M of closed topological manifolds we define torsion
obstructions whose vanishing is a necessary condition for f being homotopy
equivalent to a projection of a locally trivial fiber bundle. If N = S^1, these
torsion obstructions are identified with the ones due to Farrell.
  We have changed the exposition according to the comments of the referee and
corrected some typos. The paper will appear in Geometriae Dedicata.
