{
  "id": "2410.19091",
  "version": "v1",
  "published": "2024-10-24T18:50:41.000Z",
  "updated": "2024-10-24T18:50:41.000Z",
  "title": "Homomorphisms between large-type Artin groups",
  "authors": [
    "Martín Blufstein",
    "Alexandre Martin",
    "Nicolas Vaskou"
  ],
  "comment": "37 pages, 9 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article, we study homomorphisms between Artin groups that belong to two generic classes. For XL-type Artin groups over complete graphs, we describe all possible homomorphisms with sufficiently large image, and prove in particular that such groups are both hopfian and co-hopfian. For Artin groups with all labels at least $6$, we completely characterise in terms of the presentation graph when these groups have a finite outer automorphism group, as well as when they are co-hopfian. Moreover, when the presentation graph has no cut-vertex, we provide a generating set for their automorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-24T18:50:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F36",
      "20F67",
      "20F28"
    ],
    "keywords": [
      "large-type artin groups",
      "presentation graph",
      "finite outer automorphism group",
      "xl-type artin groups",
      "sufficiently large image"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}