{
  "id": "2402.01110",
  "version": "v2",
  "published": "2024-02-02T02:58:16.000Z",
  "updated": "2024-04-12T11:38:42.000Z",
  "title": "Homotopy Groups and Puppe Sequence of Digraphs",
  "authors": [
    "Jingyan Li",
    "Jie Wu",
    "Shing-Tung Yau",
    "Mengmeng Zhang"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We introduce homotopy groups of digraphs that admit an intuitive description of grid structures, which is a variation of the GLMY homotopy groups introduced by Grigor'yan, Lin, Muranov and Yau in [21]. Furthermore, we prove that there exists a long exact sequence of homotopy groups of digraphs associated to any based digraph map, that is, there exists a digraph version of the Puppe sequence.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-12T11:38:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q05",
      "55R65"
    ],
    "keywords": [
      "puppe sequence",
      "long exact sequence",
      "glmy homotopy groups",
      "grid structures",
      "digraph map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}