{
  "id": "1601.03992",
  "version": "v1",
  "published": "2016-01-15T16:44:22.000Z",
  "updated": "2016-01-15T16:44:22.000Z",
  "title": "Signatures for $J$-hermitians and $J$-unitaries on Krein spaces with Real structures",
  "authors": [
    "Hermann Schulz-Baldes",
    "Carlos Villegas-Blas"
  ],
  "comment": "This paper contains and considerably extends the analysis of version 1 of arXiv:1306.1816. The new version 2 of arXiv:1306.1816 only contains the applications",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "For $J$-hermitian operators on a Krein space $(\\mathcal{K},J)$ satisfying an adequate Fredholm property, a global Krein signature is shown to be a homotopy invariant. It is argued that this global signature is a generalization of the Noether index. When the Krein space has a supplementary Real structure, the sets of $J$-hermitian Fredholm operators with Real symmetry can be retracted to certain of the classifying spaces of Atiyah and Singer. Secondary $\\mathbb{Z}_2$-invariants are introduced to label their connected components. Related invariants are also analyzed for $J$-unitary operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-15T16:44:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "krein space",
      "adequate fredholm property",
      "hermitian fredholm operators",
      "supplementary real structure",
      "global krein signature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103992S"
    }
  }
}