Abstract
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 [6], 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.
Partially supported by NSF Grant DMS-9902411.
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Fisher, D. (2002). Rigid Geometric Structures and Representations of Fundamental Groups. In: Burger, M., Iozzi, A. (eds) Rigidity in Dynamics and Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04743-9_6
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DOI: https://doi.org/10.1007/978-3-662-04743-9_6
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