On Livsic's Theorem, Superrigidity, and Anosov Actions of Semisimple Lie Groups
Edward R. Goetze, Ralf J. Spatzier
Abstract
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.
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