{
  "id": "2105.01345",
  "version": "v1",
  "published": "2021-05-04T07:45:48.000Z",
  "updated": "2021-05-04T07:45:48.000Z",
  "title": "Systolic complexes and group presentations",
  "authors": [
    "Mireille Soergel"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We give conditions on a presentation of a group, which imply that its Cayley complex is simplicial and the flag complex of the Cayley complex is systolic. We then apply this to Garside groups and Artin groups. We give a classification of the Garside groups whose presentation using the simple elements as generators satisfy our conditions. We then also give a dual presentation for Artin groups and identify in which cases the flag complex of the Cayley complex is systolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-04T07:45:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "group presentations",
      "systolic complexes",
      "cayley complex",
      "garside groups",
      "artin groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}