{
  "id": "1810.11496",
  "version": "v1",
  "published": "2018-10-26T18:43:01.000Z",
  "updated": "2018-10-26T18:43:01.000Z",
  "title": "Balanced ideals and domains of discontinuity of Anosov representations",
  "authors": [
    "Florian Stecker"
  ],
  "comment": "27 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For $\\Delta$-Anosov representations, we prove that every cocompact domain of discontinuity arises from this construction, up to a few exceptions in low rank. Then we compute which flag manifolds admit these domains and, in some cases, the number of domains. We also find a new compactification for locally symmetric spaces arising from maximal representations into $\\mathrm{Sp}(4n+2, \\mathbb{R})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-26T18:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "14M15"
    ],
    "keywords": [
      "anosov representations",
      "balanced ideals",
      "semi-simple lie group",
      "construct cocompact domains",
      "flag manifolds admit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}