{
  "id": "1411.0196",
  "version": "v1",
  "published": "2014-11-02T02:45:15.000Z",
  "updated": "2014-11-02T02:45:15.000Z",
  "title": "The category of noncrossing partitions",
  "authors": [
    "Kiyoshi Igusa"
  ],
  "comment": "28 pages, 3 figures, presented at Workshop on \"Hall and cluster algebras\" May 8-12, 2014, CRM, Universite de Montreal",
  "categories": [
    "math.RT"
  ],
  "abstract": "In [13], picture groups are introduced and the cohomology of the picture group of type $A_n$ with straight orientation is computed. In this paper, we give an elementary combinatorial interpretation of the category associated to $A_n$ and prove that the classifying space of this category is a $K(\\pi,1)$. The objects of the category are the classical noncrossing partitions introduced in [19]. The morphisms are binary forests. This paper is independent of the later papers in this series except for the last section in which we compare our category with the one in [arXiv:1310.1907].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-02T02:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20"
    ],
    "keywords": [
      "picture group",
      "elementary combinatorial interpretation",
      "straight orientation",
      "binary forests",
      "classical noncrossing partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1326059,
      "adsabs": "2014arXiv1411.0196I"
    }
  }
}