Sur les actions affines des groupes discrets
Annales de l'Institut Fourier, Volume 47 (1997) no. 2, pp. 641-685.

One would hope that, for lattices in SL (n,), n3, differentiable, volume preserving actions on compact manifolds might be “classifiable”. However, we are far from realizing this goal, and so many authors have recently been considering actions of lattices in SL (n,) on manifolds of relatively low dimension, precisely, of dimension n, and which, in addition, satisfy some extra dynamical or geometrical conditions. It has been shown, for example, that there is essentially no new action, other than the standard one of SL (n,) on the n-torus. Here we generalize this fact to connection preserving actions of lattices in SL (n,) on manifolds of dimension n+1.

On pourrait espérer “classifier” les actions différentiables en préservant le volume des réseaux de SL (n,) sur les variétés compactes. On en est cependant loin. Ainsi, plusieurs auteurs ont récemment étudié les actions des réseaux de SL (n,) sur des variétés de dimension relativement basse, précisément, n, et vérifiant en plus certaines conditions géométriques ou dynamiques. On montre alors qu’il s’agit essentiellement de l’action usuelle de SL (n,) sur un tore de dimension n. Ici, on généralise ce fait aux actions des réseaux de SL (n,) sur des variétés de dimension n+1, et qui préservent une connexion.

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     title = {Sur les actions affines des groupes discrets},
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Zeghib, Abdelghani. Sur les actions affines des groupes discrets. Annales de l'Institut Fourier, Volume 47 (1997) no. 2, pp. 641-685. doi : 10.5802/aif.1577. http://archive.numdam.org/articles/10.5802/aif.1577/

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