{
  "id": "1208.2138",
  "version": "v1",
  "published": "2012-08-10T10:48:20.000Z",
  "updated": "2012-08-10T10:48:20.000Z",
  "title": "A geometric realization of the $m$-cluster category of type $\\tilde{A}$",
  "authors": [
    "Hermund André Torkildsen"
  ],
  "comment": "23 pages, 16 figures",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We give a geometric realization of a subcategory of the $m$-cluster category $\\mathcal{C}^m$ of type $\\widetilde{A}_{p,q}$, by using $(m+2)$-angulations of an annulus with $p+q$ marked points. We also give a bijection between an equivalence class of $(m+2)$-angulations and the mutation class of coloured quivers of type $\\widetilde{A}_{p,q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-10T10:48:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster category",
      "geometric realization",
      "angulations",
      "equivalence class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2138A"
    }
  }
}