{
  "id": "2203.09105",
  "version": "v1",
  "published": "2022-03-17T06:13:14.000Z",
  "updated": "2022-03-17T06:13:14.000Z",
  "title": "On Modular Cohomotopy Groups",
  "authors": [
    "Pengcheng Li",
    "Jianzhong Pan",
    "Jie Wu"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let $p$ be a prime and let $\\pi^n(X;\\mathbb{Z}/p^r)=[X,M_n(\\mathbb{Z}/p^r)]$ be the set of homotopy classes of based maps from CW-complexes $X$ into the mod $p^r$ Moore spaces $M_n(\\mathbb{Z}/p^r)$ of degree $n$, where $\\mathbb{Z}/p^r$ denotes the integers mod $p^r$. In this paper we firstly determine the modular cohomotopy groups $\\pi^n(X;\\mathbb{Z}/p^r)$ up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group $\\pi^3(X;\\mathbb{Z}_{(2)})$ with $\\dim(X)\\leq 6$ is determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T06:13:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular cohomotopy groups",
      "moore spaces",
      "primary cohomology operations",
      "integers mod",
      "extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}