{
  "id": "2106.03516",
  "version": "v1",
  "published": "2021-06-07T11:12:31.000Z",
  "updated": "2021-06-07T11:12:31.000Z",
  "title": "$\\mathbb{Z}/p^r$-hyperbolicity via homology",
  "authors": [
    "Guy Boyde"
  ],
  "comment": "31 pages. Comments welcome!",
  "categories": [
    "math.AT"
  ],
  "abstract": "We show that the homotopy groups of a Moore space $P^n(p^r)$ are $\\mathbb{Z}/p^s$-hyperbolic for $s \\leq r$ and $p^s \\neq 2$. Combined with work of Huang-Wu and Neisendorfer, this completely resolves the question of when such a Moore space is $\\mathbb{Z}/p^s$-hyperbolic for $p \\geq 5$. We also give a homological criterion for a space to be $\\mathbb{Z}/p^r$-hyperbolic, and deduce some examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-07T11:12:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q05",
      "55Q15",
      "55P40"
    ],
    "keywords": [
      "hyperbolicity",
      "moore space",
      "homotopy groups",
      "neisendorfer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}