{
  "id": "1304.5990",
  "version": "v2",
  "published": "2013-04-22T15:47:41.000Z",
  "updated": "2016-01-05T14:34:24.000Z",
  "title": "The 6-strand braid group is CAT(0)",
  "authors": [
    "Thomas Haettel",
    "Dawid Kielak",
    "Petra Schwer"
  ],
  "comment": "27 pages, 13 figures. To appear in Geometriae Dedicata, the final publication is available at Springer via http://dx.doi.org/10.1007/s10711-015-0138-9",
  "doi": "10.1007/s10711-015-0138-9",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability of their diagonal links into spherical buildings of type A. Furthermore, we prove that the orthoscheme complex of any bounded graded modular complemented lattice is CAT(0), giving a partial answer to a conjecture of Brady and McCammond.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-22T15:47:41.000Z",
      "comment": "19 pages, 9 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-05T14:34:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "51M20",
      "06A11",
      "06C20",
      "05A18"
    ],
    "keywords": [
      "braid group",
      "orthoscheme complex",
      "close connection",
      "associated non-crossing partition complexes",
      "diagonal links"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5990H"
    }
  }
}