{
  "id": "1508.03699",
  "version": "v1",
  "published": "2015-08-15T05:53:06.000Z",
  "updated": "2015-08-15T05:53:06.000Z",
  "title": "On the structure of braid groups on complexes",
  "authors": [
    "Byung Hee An",
    "Hyo Won Park"
  ],
  "comment": "40 pages, 26 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider the braid groups $\\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for $X$ and their effects on braid groups, and provide an algorithmic way to compute the group presentations for $\\mathbf{B}_n(X)$ with the aid of them. As applications, we give complete criteria for both the surface embeddability and planarity for $X$, which are the torsion-freeness of the braid group $\\mathbf{B}_n(X)$ and its abelianization $H_1(\\mathbf{B}_n(X))$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-15T05:53:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "05E45",
      "57M20"
    ],
    "keywords": [
      "braid group",
      "finite simplicial complexes",
      "geometric decompositions",
      "algorithmic way",
      "group presentations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}