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Smooth factors of projective actions of higher-rank lattices and rigidity. (English) Zbl 1384.37033

The authors study smooth factors of the standard actions of lattices in higher-rank semisimple Lie groups on flag manifolds. Under a condition on the existence of a single differentiable sink, they show that these factors are \(C^\infty\)-conjugate to the standard actions on flag manifolds. As an application, they also get some local rigidity results.

MSC:

37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
14M15 Grassmannians, Schubert varieties, flag manifolds
06F30 Ordered topological structures
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
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