{
  "id": "2007.16155",
  "version": "v1",
  "published": "2020-07-31T16:15:11.000Z",
  "updated": "2020-07-31T16:15:11.000Z",
  "title": "Renormalization groupoids in algebraic topology",
  "authors": [
    "Jack Morava"
  ],
  "comment": "Comments very welcome",
  "categories": [
    "math.AT"
  ],
  "abstract": "Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $M\\xi$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for complex-oriented quasitoric manifolds, and show that automorphisms or cohomology operations on this representation are defined by a `renormalization' Hopf algebra of formal diffeomorphisms at the origin of the noncommutative line, previously considered (over $Q$) in quantum electrodynamics. The resulting structure can be presented in purely algebraic terms, as a groupoid scheme over $Z$ defined by a coaction of this Hopf algebra on the ring of noncommutative symmetric functions. We sketch some applications to symplectic toric manifolds, combinatorics of simplicial spheres, and statistical mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-31T16:15:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16Txx",
      "55N22",
      "82B30"
    ],
    "keywords": [
      "algebraic topology",
      "renormalization groupoids",
      "richters noncommutative complex cobordism spectrum",
      "hopf algebra",
      "symplectic toric manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}