{
  "id": "2001.11872",
  "version": "v1",
  "published": "2020-01-31T14:43:04.000Z",
  "updated": "2020-01-31T14:43:04.000Z",
  "title": "Bounding size of homotopy groups of spheres",
  "authors": [
    "Guy Boyde"
  ],
  "comment": "5 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $p$ be prime. We prove that, for $n$ odd, the $p$-torsion part of $\\pi_q(S^{n})$ has cardinality at most $p^{2^{\\frac{1}{p-1}(q-n+3-2p)}}$, and hence has rank at most $2^{\\frac{1}{p-1}(q-n+3-2p)}$. For $p=2$ these results also hold for $n$ even. The best bounds in the existing literature are $p^{2^{q-n+1}}$ and $2^{q-n+1}$ respectively, both due to Hans-Werner Henn. The main point of our result is therefore that the bound grows more slowly for larger primes. As a corollary of work of Henn, we obtain a similar result for the homotopy groups of a broader class of spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-31T14:43:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q40"
    ],
    "keywords": [
      "homotopy groups",
      "bounding size",
      "broader class",
      "similar result",
      "torsion part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}