{
  "id": "2407.19940",
  "version": "v1",
  "published": "2024-07-29T12:21:48.000Z",
  "updated": "2024-07-29T12:21:48.000Z",
  "title": "Rigidity and classification results for large-type Artin groups",
  "authors": [
    "Jingyin Huang",
    "Damian Osajda",
    "Nicolas Vaskou"
  ],
  "comment": "52 pages, 9 figures",
  "categories": [
    "math.GR",
    "math.GT",
    "math.OA"
  ],
  "abstract": "We compute the automorphism group of the intersection graph of many large-type Artin groups. This graph is an analogue of the curve graph of mapping class groups but in the context of Artin groups. As an application, we deduce a number of rigidity and classification results for these groups, including computation of outer automorphism groups, commensurability classification, quasi-isometric rigidity, measure equivalence rigidity, orbit equivalence rigidity, rigidity of lattice embedding, and rigidity of cross-product von Neumann algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T12:21:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F65",
      "20F28",
      "20E36",
      "37A20",
      "46L36"
    ],
    "keywords": [
      "large-type artin groups",
      "classification results",
      "cross-product von neumann algebra",
      "measure equivalence rigidity",
      "outer automorphism groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}