{
  "id": "2405.12717",
  "version": "v1",
  "published": "2024-05-21T12:19:34.000Z",
  "updated": "2024-05-21T12:19:34.000Z",
  "title": "A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups",
  "authors": [
    "Eiolf Kaspersen",
    "Gereon Quick"
  ],
  "comment": "11 pages, comments very welcome",
  "categories": [
    "math.AT"
  ],
  "abstract": "We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their classifying spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-21T12:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R77",
      "57T10",
      "55R35",
      "55S05",
      "55S10"
    ],
    "keywords": [
      "classifying space",
      "gauge group",
      "detect nontrivial elements",
      "exceptional lie groups",
      "non-torsion generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}