Rigid Geometric Structures and Representations of Fundamental Groups
Let G be a simple Lie group, ℝ-rank(G) ≥ 2, and F < G a lattice. Assume that Γ acts analytically and ergodically on a compact manifold M preserving a volume and an analytic rigid geometric structure. In , we establish that either the Γ-action is isometric and π1(M) is finite or π1(M) admits a “large image” linear representation. We discuss the proof of this result. We also present related results which use similar techniques to show that under slightly stronger hypotheses the Γ-action is a 0-entropy extension of a standard arithmetic example. We give one new result in which this extension can be shown to be continuous rather than measurable.
KeywordsFundamental Group Compact Manifold Lattice Action Zariski Closure Finite Cover
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