{
  "id": "1701.02130",
  "version": "v1",
  "published": "2017-01-09T11:03:10.000Z",
  "updated": "2017-01-09T11:03:10.000Z",
  "title": "On the bottom of spectra under coverings",
  "authors": [
    "Werner Ballmann",
    "Henrik Matthiesen",
    "Panagiotis Polymerakis"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DG",
    "math.SP"
  ],
  "abstract": "For a Riemannian covering $M_1\\to M_0$ of complete Riemannian manifolds with boundary (possibly empty) and respective fundamental groups $\\Gamma_1\\subseteq\\Gamma_0$, we show that the bottoms of the spectra of $M_0$ and $M_1$ coincide if the right action of $\\Gamma_0$ on $\\Gamma_1\\backslash\\Gamma_0$ is amenable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-09T11:03:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifolds",
      "respective fundamental groups",
      "right action",
      "possibly empty"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}