{
  "id": "math-ph/0005027",
  "version": "v1",
  "published": "2000-05-26T14:53:40.000Z",
  "updated": "2000-05-26T14:53:40.000Z",
  "title": "Supersymmetry and Homotopy",
  "authors": [
    "Serge Maumary",
    "Izumi Ojima"
  ],
  "categories": [
    "math-ph",
    "math.AT",
    "math.MP"
  ],
  "abstract": "The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes' programme where a geometrical structure is rigidly fixed. For instance, we can relate supersymmetries of types N=2n and N=(n, n) in spite of their gap due to distinction between $\\Bbb{Z}_2$(even-odd)- and integer-gradings. Our approach goes beyond the theory of real homotopy due to Quillen, Sullivan and Tanr\\'e developed, respectively, in the 60's, 70's and 80's, which exhibits real homotopy of a 1-connected space out of its de Rham-Fock complex with supersymmetry. Our main new step is based upon the Taylor (super-)expansion and locality, which links differential geometry with homotopy without the restriction of 1-connectedness. While the homotopy invariants treated so far in relation with supersymmetry are those depending only on $\\Bbb{Z}_2$-grading like the index, here we can detect new $\\Bbb{N}$-graded homotopy invariants. While our setup adopted here is (graded) commutative, it can be extended also to the non-commutative cases in use of state germs (Haag-Ojima) corresponding to a Taylor expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-05-26T14:53:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetry",
      "real homotopy",
      "links differential geometry",
      "taylor expansion",
      "supersymmetric structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 528277,
      "adsabs": "2000math.ph...5027M"
    }
  }
}