{
  "id": "math/0408213",
  "version": "v1",
  "published": "2004-08-16T21:30:30.000Z",
  "updated": "2004-08-16T21:30:30.000Z",
  "title": "Local rigidity of affine actions of higher rank groups and lattices",
  "authors": [
    "David Fisher",
    "Gregory Margulis"
  ],
  "comment": "59 pages",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\\Gamma<J$ 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 $\\Ta^n$ on which it acts by automorphisms, we show that the diagonal action on $\\Ta^n{\\times}M$ is locally rigid. This paper is the culmination of a series of papers and depends heavily on our work in \\cite{FM1,FM2}. The reader willing to accept the main results of those papers as \"black boxes\" should be able to read the present paper without referring to them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-16T21:30:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "53C24"
    ],
    "keywords": [
      "higher rank groups",
      "affine actions",
      "locally rigid",
      "general local rigidity result",
      "semisimple lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8213F"
    }
  }
}