{
  "id": "2305.11622",
  "version": "v1",
  "published": "2023-05-19T12:02:53.000Z",
  "updated": "2023-05-19T12:02:53.000Z",
  "title": "New Garside structures and applications to Artin groups",
  "authors": [
    "Thomas Haettel",
    "Jingyin Huang"
  ],
  "comment": "38 pages, 3 figures. Comments welcome!",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Garside groups are combinatorial generalizations of braid groups which enjoy many nice algebraic, geometric, and algorithmic properties. In this article we propose a method for turning the direct product of a group $G$ by $\\mathbb{Z}$ into a Garside group, under simple assumptions on $G$. This method gives many new examples of Garside groups, including groups satisfying certain small cancellation condition (including surface groups) and groups with a systolic presentation. Our method also works for a large class of Artin groups, leading to many new group theoretic, geometric and topological consequences for them. In particular, we prove new cases of $K(\\pi,1)$-conjecture for some hyperbolic type Artin groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-19T12:02:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E42",
      "20F36",
      "20F55",
      "05B35",
      "06A12",
      "20F65",
      "05C25"
    ],
    "keywords": [
      "garside structures",
      "garside group",
      "applications",
      "hyperbolic type artin groups",
      "small cancellation condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}