Rigidity and cocycles for ergodic actions of semi-simple lie groups Page 1 S6minaire
BOURBAKI 32e annie, 1979/80, n 559 559-O1 Juin 1980 RIGIDITY AND COCYCLES FOR …

A conference on the interaction of ergodic theory, differential geometry and the theory of Lie
Groups was held at the Mathematical Sciences Research Institute from May 24 to June 1 …

The aim of this paper is to prove an analogue of the strong rigidity theorems for lattices in
semisimple Lie groups of Mostow and Margulis in the context of ergodic actions of …

1. Introduction. The point of this paper is to study the low dimensional cohomology theory of
ergodic actions of semisimple Lie groups and their lattice subgroups. The rigidity theorem for …

Let M be a smooth manifold, G a geometric structure on M, and G a Lie group that acts on M
so as to leave G invariant. In other words, G is a group of isometries of (M, G). The subject of …

In a series of recent papers [21-23], we have examined certain rigidity properties of actions
of semisimple Lie groups and their discrete subgroups on compact manifolds. In these …

An important problem in ergodic theory is to determine when the restriction to a subgroup of
an ergodic action of a group is still ergodic. Classical results concerning the ergodicity of …

Suppose G is a connected, simple, real Lie group with R-rank (G)≥ 2, M is an ergodic G-
space with invariant probability measure μ, and α: G× M→ Homeo (T) is a Borel cocycle. We …

Smooth actions of certain Lie groups are (vaguely) conjectured to be “rigid”. In considering
such conjectures it is natural to start by studying actions that are already rigid. Indeed from …

Let G be a connected Lie group and\mathcal {C}(G) be the space of all closed subgroups of
G, equipped with the Fell topology. We consider actions on\mathcal {C}(G), of G (by …