Deformations of group actions

David Fisher

Published 2004-07-24, updated 2006-07-16Version 2

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when $G=SO(1,n)$ and provide a simple proof that any action of a compact Lie group is locally rigid.