{
  "id": "1502.01232",
  "version": "v1",
  "published": "2015-02-04T15:34:28.000Z",
  "updated": "2015-02-04T15:34:28.000Z",
  "title": "Differential geometric invariants for time-reversal symmetric Bloch-bundles: the \"Real\" case",
  "authors": [
    "Giuseppe De Nittis",
    "Kiyonori Gomi"
  ],
  "comment": "49 pages. key words: Topological quantum systems, Bloch-bundle, \"Real and \"Quaternionic\" vector bundles , equivariant connections, \"Real\" Chern-Weil theory",
  "categories": [
    "math-ph",
    "cond-mat.mes-hall",
    "math.MP"
  ],
  "abstract": "Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related \"Real\" (resp. \"Quaternionic\") Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in [DG1] for the \"Real\" case and in [DG2] for the \"Quaternionic\" case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article (and its companion [DG3]) we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the \"Real\" case we generalize the Chern-Weil theory and we showed that the assignment of a \"Real\" connection, along with the related differential Chern class and its holonomy, suffices for the classification of \"Real\" vector bundles in low dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-04T15:34:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R22",
      "53A55",
      "55N25",
      "53C80"
    ],
    "keywords": [
      "differential geometric invariants",
      "time-reversal symmetric bloch-bundles",
      "time-reversal vector bundle theories",
      "time-reversal symmetry",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150201232D"
    }
  }
}