Séminaire de géométrie - Salle de conférences Jean Lascoux (CPHT) - 14h

«Zimmer's conjecture for non-split semisimple Lie groups» 

Résumé : Mostow's Rigidity Theorem states that two closed hyperbolic manifolds of dimension n≥3 with isomorphic fundamental groups are isometric, which can also be understood as a rigidity statement for action of lattice in PO(n,1) on H^n by isometries. This has been further generalized to Margulis' Superrigidity Theorem.  In an attempt to understand the rigidity phenomenon for higher rank lattice action by diffeomorphisms on manifold, Zimmer has conjectured that a higher rank lattice in a semisimple Lie group cannot have essentially non-trivial action on manifolds with dimension smaller than certain quantity related to the Lie algebra. This conjecture is proved in many cases by Aaron Brown, David Fisher and Sebastian Hurtado. Their result provides sharp dimension bounds for real split semisimple real Lie groups but not sharp otherwise. We discuss a recent generalisation of their result with sharp bounds to some other (non-real split) semisimple Lie groups. This is a joint work with Jinpeng An and Aaron Brown.