{
  "id": "2209.03860",
  "version": "v1",
  "published": "2022-09-08T14:59:51.000Z",
  "updated": "2022-09-08T14:59:51.000Z",
  "title": "Graph of groups decompositions of graph braid groups",
  "authors": [
    "Daniel Berlyne"
  ],
  "comment": "33 pages, 14 figures. Comments welcome!",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-08T14:59:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20F36"
    ],
    "keywords": [
      "graph braid group",
      "groups decompositions",
      "non-trivial free product",
      "explicit construction",
      "explicit example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}