{
  "id": "1311.6680",
  "version": "v1",
  "published": "2013-11-26T14:11:33.000Z",
  "updated": "2013-11-26T14:11:33.000Z",
  "title": "Poset topology and homological invariants of algebras arising in algebraic combinatorics",
  "authors": [
    "Stuart Margolis",
    "Franco Saliola",
    "Benjamin Steinberg"
  ],
  "comment": "This is an extended abstract surveying the results of arXiv:1205.1159 and an article in preparation. 12 pages, 3 Figures",
  "categories": [
    "math.CO",
    "math.GR",
    "math.RA",
    "math.RT"
  ],
  "abstract": "We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay. For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra. R\\'esum\\'e. Nous pr\\'esentons une magnifique interaction entre la topologie combinatoire et l'alg\\`ebre homologique d'une classe de mono\\\"ides qui figurent naturellement dans la combinatoire alg\\'ebrique. Nous explorons plusieurs applications de cette interaction. Par exemple, nous introduisons une nouvelle interpr\\'etation du nombre de Leray d'un complexe de clique en termes de la dimension globale d'une certaine alg\\`ebre non commutative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-26T14:11:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "16E10",
      "16G10",
      "52C35",
      "05E45"
    ],
    "keywords": [
      "algebraic combinatorics",
      "poset topology",
      "homological invariants",
      "algebras arising",
      "dimension globale dune certaine"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6680M"
    }
  }
}