{
  "id": "1707.02481",
  "version": "v1",
  "published": "2017-07-08T19:02:48.000Z",
  "updated": "2017-07-08T19:02:48.000Z",
  "title": "Trees, homology, and automorphism groups of RAAGs",
  "authors": [
    "Javier Aramayona",
    "José L. Fernández",
    "Pablo Fernández",
    "Conchita Martínez-Pérez"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-08T19:02:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "automorphism group",
      "explicit finite-index subgroup",
      "first betti number",
      "average value",
      "combinatorial methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}