Article

# Deformations of group actions

08/2004;
Source: arXiv

ABSTRACT 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.

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### Keywords

compact Lie group

deformations

noncompact real algebraic group

simple proof

smooth

smooth deformation