{
  "id": "2203.10371",
  "version": "v1",
  "published": "2022-03-19T18:26:29.000Z",
  "updated": "2022-03-19T18:26:29.000Z",
  "title": "A generalization of the Hopf degree theorem",
  "authors": [
    "Matthew D. Kvalheim"
  ],
  "comment": "2 pages, comments welcome",
  "categories": [
    "math.GT",
    "math.AT",
    "math.DG"
  ],
  "abstract": "The Hopf degree theorem states that homotopy classes of continuous maps from a smooth connected closed $n$-manifold $M$ to the $n$-sphere are classified by their degree when $M$ is oriented and by their mod $2$ degree when $M$ is nonorientable. Such a map is equivalent to a section of the trivial $n$-sphere bundle over $M$. A generalization of the Hopf degree theorem is obtained for the case that the sphere bundle over $M$ is nontrivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-19T18:26:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "55R25",
      "55N45"
    ],
    "keywords": [
      "generalization",
      "hopf degree theorem states",
      "sphere bundle",
      "homotopy classes",
      "nontrivial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}