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H 1 Rigidity of hyperbolic higher rank lattice actions

Auteurs : Rodriguez Hertz, Federico (Auteur de la Conférence)
CIRM (Editeur )

Résumé : I will discuss some recent results with Aaron Brown and Zhiren Wang on actions by higher rank lattices on nilmanifolds. I will present the result in the simplest case possible, $SL(n,Z)$ acting on $Tn$, and try to present the ideas of the proof. The result imply existence of invariant measures for $SL(n,Z)$ actions on $Tn$ with standard homotopy data as well as global rigidity of Ansosov actions on infranilmanifolds and existence of semiconjugacies without assumption on existence of invariant measure.