{
  "id": "2110.02458",
  "version": "v2",
  "published": "2021-10-06T02:09:38.000Z",
  "updated": "2022-04-27T01:25:10.000Z",
  "title": "Magnitude homology of graphs and discrete Morse theory on Asao-Izumihara complexes",
  "authors": [
    "Yu Tajima",
    "Masahiko Yoshinaga"
  ],
  "categories": [
    "math.AT",
    "math.CO",
    "math.MG"
  ],
  "abstract": "Recently, Asao and Izumihara introduced CW-complexes whose homology groups are isomorphic to direct summands of the graph magnitude homology group. In this paper, we study the homotopy type of the CW-complexes in connection with the diagonality of magnitude homology groups. We prove that the Asao-Izumihara complex is homotopy equivalent to a wedge of spheres for pawful graphs introduced by Y. Gu. The result can be considered as a homotopy type version of Gu's result. We also formulate a slight generalization of the notion of pawful graphs and find new non-pawful diagonal graphs of diameter $2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-27T01:25:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N35",
      "05C10",
      "51F99",
      "05E45"
    ],
    "keywords": [
      "discrete morse theory",
      "asao-izumihara complex",
      "graph magnitude homology group",
      "pawful graphs",
      "homotopy type version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}