{
  "id": "2409.06408",
  "version": "v1",
  "published": "2024-09-10T10:45:00.000Z",
  "updated": "2024-09-10T10:45:00.000Z",
  "title": "A note on invariants of foliated 3-sphere bundles",
  "authors": [
    "Nils Prigge"
  ],
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "In this note we prove that $H^*(\\text{BSO}(4);\\mathbb{Q})$ injects into the group cohomology of $\\text{Diff}^+(S^{3})$ with rational coefficients. The proof is based on an idea of Nariman who proved that the monomials in the Euler and Pontrjagin classes are nontrivial in $H^*(\\text{BDiff}_+^{\\delta}(S^{2n-1});\\mathbb{Q})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-10T10:45:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariants",
      "group cohomology",
      "rational coefficients",
      "pontrjagin classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}