{
  "id": "2101.03060",
  "version": "v1",
  "published": "2021-01-08T15:26:39.000Z",
  "updated": "2021-01-08T15:26:39.000Z",
  "title": "Convex cores for actions on finite-rank median algebras",
  "authors": [
    "Elia Fioravanti"
  ],
  "comment": "28 pages, no figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty \"convex core\", even when no metric or topology is given. We then use this to deduce an analogue of the flat torus theorem for actions on connected finite-rank median spaces. We also prove that isometries of connected finite-rank median spaces are either elliptic or loxodromic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-08T15:26:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex core",
      "connected finite-rank median spaces",
      "finite-rank median algebra admits",
      "flat torus theorem",
      "finitely generated group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}