{
  "id": "2301.12963",
  "version": "v1",
  "published": "2023-01-30T15:06:22.000Z",
  "updated": "2023-01-30T15:06:22.000Z",
  "title": "On Sharp Bounds for the Dynamic Asymptotic Dimension",
  "authors": [
    "SJ Pilgrim"
  ],
  "comment": "17 pages, comments welcome",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We prove the dynamic asymptotic dimension of a free isometric action on a space of finite doubling dimension is either infinite or equal to the asymptotic dimension of the acting group; and give a full description of the dynamic asymptotic dimension of translation actions on compact Lie groups in terms of the amenability and asymptotic dimension of the acting group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T15:06:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "46L05"
    ],
    "keywords": [
      "dynamic asymptotic dimension",
      "sharp bounds",
      "compact lie groups",
      "free isometric action",
      "acting group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}