{
  "id": "hep-th/0508084",
  "version": "v2",
  "published": "2005-08-11T14:00:23.000Z",
  "updated": "2006-02-02T00:59:51.000Z",
  "title": "T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group",
  "authors": [
    "Varghese Mathai",
    "Jonathan Rosenberg"
  ],
  "comment": "Latex2e, 36 pages, 2 figures, uses xypic, few minor changes made",
  "journal": "Adv.Theor.Math.Phys. 10 (2006) 123-158",
  "categories": [
    "hep-th",
    "math.AT",
    "math.OA"
  ],
  "abstract": "We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a \"classical\" T-dual, i.e., a dual bundle with dual H-flux, and when the T-dual must be \"non-classical,\" that is, a continuous field of noncommutative tori. The duality comes with an isomorphism of twisted $K$-theories, required for matching of D-brane charges, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced in the non-classical case by an isomorphism of twisted cyclic homology. An important part of the paper contains a detailed analysis of the classifying space for topological T-duality, as well as the T-duality group and its action. The issue of possible non-uniqueness of T-duals can be studied via the action of the T-duality group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-02T00:59:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "t-duality group",
      "noncommutative topology",
      "high-dimensional case",
      "principal torus bundles",
      "classical case"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4310/ATMP.2006.v10.n1.a5"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 689667,
      "adsabs": "2005hep.th....8084M"
    }
  }
}