On Livsic's Theorem, Superrigidity, and Anosov Actions of Semisimple Lie   Groups
  We prove a generalization of Livsic's Theorem on the vanishing of the cohomology of certain types of dynamical systems. As a consequence, we strengthen a result due to Zimmer concerning algebraic hulls of Anosov actions of semisimple Lie groups. Combining this with Topological Superrigidity, we find a Holder geometric structure for multiplicity free Anosov actions. 
Edward R. Goetze and Ralf J. Spatzier