{
  "id": "2101.04591",
  "version": "v1",
  "published": "2021-01-12T16:42:46.000Z",
  "updated": "2021-01-12T16:42:46.000Z",
  "title": "$p$-hyperbolicity of homotopy groups via $K$-theory",
  "authors": [
    "Guy Boyde"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We show that $S^n \\vee S^m$ is $\\mathbb{Z}/p^r$-hyperbolic for all primes $p$ and all $r \\in \\mathbb{N}$, provided $n,m \\geq 2$, and consequently that various spaces containing $S^n \\vee S^m$ as a $p$-local retract are $\\mathbb{Z}/p^r$-hyperbolic. We then give a $K$-theory criterion for a suspension $\\Sigma X$ to be $p$-hyperbolic, and use it to deduce that the suspension of a complex Grassmannian $\\Sigma Gr_{k,n}$ is $p$-hyperbolic for all odd primes $p$ when $n \\geq 3$ and $0<k<n$. We obtain similar results for some related spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T16:42:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q52",
      "55Q15",
      "19L20"
    ],
    "keywords": [
      "homotopy groups",
      "hyperbolicity",
      "similar results",
      "theory criterion",
      "suspension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}