{
  "id": "1803.00416",
  "version": "v1",
  "published": "2018-03-01T15:00:01.000Z",
  "updated": "2018-03-01T15:00:01.000Z",
  "title": "Embeddability and quasi-isometric classification of partially commutative groups",
  "authors": [
    "Montserrat Casals-Ruiz"
  ],
  "journal": "Algebraic & Geometric Topology 16 (2016) 597-620",
  "doi": "10.2140/agt.2016.16.597",
  "categories": [
    "math.GR"
  ],
  "abstract": "The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups $\\mathbb{G}(\\Delta)$ and $\\mathbb{G}(\\Gamma)$ are quasi-isometric, then $\\mathbb{G}(\\Delta)$ is a (nice) subgroup of $\\mathbb{G}(\\Gamma)$ and vice-versa. We show that the conjecture holds for all known cases of quasi-isometric classification of partially commutative groups, namely for the classes of $n$-tress and atomic graphs. As in the classical Mostow rigidity theory for irreducible lattices, we relate the quasi-isometric rigidity of the class of atomic partially commutative groups with the algebraic rigidity, that is with the co-Hopfian property of their $\\mathbb{Q}$-completions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-01T15:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partially commutative groups",
      "quasi-isometric classification",
      "embeddability",
      "alias right-angled artin groups",
      "classical mostow rigidity theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}