{
  "id": "1905.07142",
  "version": "v1",
  "published": "2019-05-17T07:30:22.000Z",
  "updated": "2019-05-17T07:30:22.000Z",
  "title": "On balanced coronas of groups",
  "authors": [
    "Igor Protasov"
  ],
  "comment": "coarse structure, slowly oscillating functions, balanced corona",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $G$ be an infinite group, $\\kappa$ be an infinite cardinal, $\\kappa\\leq \\mid G\\mid$ and let $\\mathcal{E}_{\\kappa}$ denotes a coarse structure on $G$ with the base $\\{\\{ (x,y): y\\in F x F\\}: F\\in [G]^{<\\kappa}\\}$. We prove that if either $\\kappa< \\mid G\\mid$ or $\\kappa= \\mid G\\mid$ and $\\kappa$ is singular then the Higson's corona $\\nu _{\\kappa} (G)$ of the coarse space $(G, \\mathcal{E}_{\\kappa})$ is a singleton. If $\\kappa= \\mid G\\mid$ and $\\kappa$ is regular then $\\nu _{\\kappa} (G)$ contains a copy of the space $U_{\\kappa}$ of $\\kappa$-uniform ultrafilters on $\\kappa$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-17T07:30:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "balanced coronas",
      "infinite cardinal",
      "coarse structure",
      "infinite group",
      "higsons corona"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}