Geodesic
Local rigidity of affine actions of higher rank groups and lattices
David Fisher1 ; Gregory Margulis2
1 Indiana University<br/>Department of Mathematics<br/>Rawles Hall<br/>Bloomington, IN 47401<br/>United States
2 Yale University<br/>Department of Mathematics<br/>P.O. Box 208283<br/>New Haven, CT 06520<br/>United States
Annals of mathematics, Tome 170 (2009) no. 1, pp. 67-122.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\Gamma\lt J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $\Gamma$. This shows that almost all so-called “standard actions” are locally rigid. As a special case, we see that any action of $\Gamma$ by toral automorphisms is locally rigid. More generally, given a manifold $M$ on which $\Gamma$ acts isometrically and a torus $\mathbb T^n$ on which it acts by automorphisms, we show that the diagonal action on $\mathbb T^n{\times}M$ is locally rigid.
DOI : 10.4007/annals.2009.170.67

David Fisher 1 ; Gregory Margulis 2

1 Indiana University<br/>Department of Mathematics<br/>Rawles Hall<br/>Bloomington, IN 47401<br/>United States
2 Yale University<br/>Department of Mathematics<br/>P.O. Box 208283<br/>New Haven, CT 06520<br/>United States 
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David Fisher; Gregory Margulis. Local rigidity of affine actions of higher rank groups and lattices. Annals of mathematics, Tome 170 (2009) no. 1, pp. 67-122. doi : 10.4007/annals.2009.170.67. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.67/

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