  Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts
continuously on a manifold M, with fundamental group Z^n, preserving a measure
that is positive on open sets. Further assume that the induced G action on
H^1(M) is non-trivial. We show there exists a finite index subgroup G' of G and
a G' equivariant continuous map from M to the n-torus that induces an
isomorphism on fundamental groups.
  We prove more general results providing continuous quotients in cases where
the fundamental group of M surjects onto a finitely generated torsion free
nilpotent group. We also give some new examples of manifolds with G actions to
which the theorems apply.
