Local rigidity of affine actions of higher rank groups and lattices
Annals of mathematics, Tome 170 (2009) no. 1, pp. 67-122
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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.
@article{10_4007_annals_2009_170_67,
author = {David Fisher and Gregory Margulis},
title = {Local rigidity of affine actions of higher rank groups and lattices},
journal = {Annals of mathematics},
pages = {67--122},
publisher = {mathdoc},
volume = {170},
number = {1},
year = {2009},
doi = {10.4007/annals.2009.170.67},
mrnumber = {2521112},
zbl = {1186.22015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.67/}
}
TY - JOUR AU - David Fisher AU - Gregory Margulis TI - Local rigidity of affine actions of higher rank groups and lattices JO - Annals of mathematics PY - 2009 SP - 67 EP - 122 VL - 170 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.67/ DO - 10.4007/annals.2009.170.67 LA - en ID - 10_4007_annals_2009_170_67 ER -
%0 Journal Article %A David Fisher %A Gregory Margulis %T Local rigidity of affine actions of higher rank groups and lattices %J Annals of mathematics %D 2009 %P 67-122 %V 170 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.67/ %R 10.4007/annals.2009.170.67 %G en %F 10_4007_annals_2009_170_67
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
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