Deformations of group actions

Fisher, David

doi:10.1090/S0002-9947-07-04372-3

Deformations of group actions
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Trans. Amer. Math. Soc. 360 (2008), 491-505 Request permission

Abstract:

Let $G$ be a non-compact real algebraic group and $\Gamma <G$ a lattice. One purpose of this paper is to show that there is a smooth, volume preserving, mixing action of $G$ or $\Gamma$ on a compact manifold which admits a smooth deformation. In fact, we prove a stronger statement by exhibiting large finite dimensional spaces of deformations. We also describe some other, rather special, deformations when $G=SO(1,n)$.

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