{
  "id": "2401.00654",
  "version": "v1",
  "published": "2024-01-01T03:49:36.000Z",
  "updated": "2024-01-01T03:49:36.000Z",
  "title": "Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center",
  "authors": [
    "Sven Sandfeldt"
  ],
  "comment": "64 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_{\\Gamma}$. We show that, under certain natural assumptions, all such actions are $C^{\\infty}-$conjugated to an affine model. Along the way, we also prove two results of independent interest. We describe fibered partially hyperbolic diffeomorphisms on $X_{\\Gamma}$ and we show that topological conjugacies between partially hyperbolic actions and higher rank affine actions are $C^{\\infty}$. As a consequence, we obtain a centralizer rigidity result, and we classify all possible centralizers for any $C^{1}-$small perturbation of an irreducible, affine partially hyperbolic map on such manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-01T03:49:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "37D30",
      "37C15",
      "53C24"
    ],
    "keywords": [
      "partially hyperbolic abelian actions",
      "global rigidity",
      "abelian partially hyperbolic higher rank",
      "higher rank affine actions",
      "partially hyperbolic higher rank actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}