{
  "id": "2009.11909",
  "version": "v1",
  "published": "2020-09-24T19:07:41.000Z",
  "updated": "2020-09-24T19:07:41.000Z",
  "title": "The character map in (twisted differential) non-abelian cohomology",
  "authors": [
    "Domenico Fiorenza",
    "Hisham Sati",
    "Urs Schreiber"
  ],
  "comment": "116 pages",
  "categories": [
    "math.AT",
    "hep-th",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham cohomology of twisted L-infinity algebra valued differential forms. The construction amounts to leveraging the fundamental theorem of dg-algebraic rational homotopy theory to a twisted non-abelian generalization of the de Rham theorem. We show that the non-abelian character reproduces, besides the Chern-Dold character, also the Chern-Weil homomorphism as well as its secondary Cheeger-Simons homomorphism on (differential) non-abelian cohomology in degree 1, represented by principal bundles (with connection); and thus generalizes all these to higher (twisted, differential) non-abelian cohomology, represented by higher bundles/higher gerbes (with higher connections). As a fundamental example, we discuss the twisted non-abelian character map on twistorial Cohomotopy theory over 8-manifolds, which can be viewed as a twisted non-abelian enhancement of topological modular forms (tmf) in degree 4. This turns out to exhibit a list of subtle topological relations that in high energy physics are thought to govern the charge quantization of fluxes in M-theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-24T19:07:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-abelian cohomology",
      "character map",
      "twisted differential",
      "twisted non-abelian",
      "chern-dold character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 116,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}