{
  "id": "2404.10701",
  "version": "v1",
  "published": "2024-04-16T16:18:00.000Z",
  "updated": "2024-04-16T16:18:00.000Z",
  "title": "Spectra of subrings of cohomology generated by characteristic classes for fusion systems",
  "authors": [
    "Ian J. Leary",
    "Jason Semeraro"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "If $\\mathcal{F}$ is a saturated fusion system on a finite $p$-group $S$, we define the Chern subring $Ch(\\mathcal{F})$ of $\\mathcal{F}$ to be the subring of the mod-$p$ cohomology $H^*(S)$ of $S$ generated by the Chern classes of $\\mathcal{F}$-stable representations of $S$. We show that $Ch(\\mathcal{F})$ is contained in $H^*(\\mathcal{F})$ and apply a result of Green and the first author to describe its spectrum in terms of a certain category of elementary abelian subgroups of $S$. We obtain similar results for various related subrings, including those generated by characteristic classes of $\\mathcal{F}$-stable $S$-sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-16T16:18:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "20D20"
    ],
    "keywords": [
      "characteristic classes",
      "cohomology",
      "elementary abelian subgroups",
      "first author",
      "saturated fusion system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}