GLOBAL RIGIDITY RESULTS FOR LATTICE ACTIONS ON TORI AND NEW EXAMPLES OF VOLUME-PRESERVING ACTIONS

Any action of a finite index subgroup in SL(n, Z), n greater than or e qual to 4 on the n-dimensional torus which has a finite orbit and cont ains an Anosov element which splits as a direct product is smoothly co njugate to an affine action. We also construct first examples of real- analytic volume-preserving actions of SL(n, Z) and other higher-rank l attices on compact manifolds which are not conjugate (even topological ly) to algebraic models.