Abstract:
In joint work with G.A.Margulis, we have proven many results showing that smooth actions of "large groups" on compact manifolds are locally rigid. By local rigidity we mean that any perturbation of the action is conjugate back to the original action by a diffeomorphism.
I will begin by describing our general results and discussing the context and motivation for this work. Then, in order to be able to describe some of the ideas in the proof, I will concentrate on the following:
Theorem. Let G be a group with property (T) of Kazhdan. Then any isometric action of G on a compact Riemannian manifold is locally rigid.