{
  "id": "1301.5811",
  "version": "v1",
  "published": "2013-01-24T15:17:39.000Z",
  "updated": "2013-01-24T15:17:39.000Z",
  "title": "The kernel bundle of a holomorphic Fredholm family",
  "authors": [
    "Thomas Krainer",
    "Gerardo A. Mendoza"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $\\Y$ be a smooth connected manifold, $\\Sigma\\subset\\C$ an open set and $(\\sigma,y)\\to\\scrP_y(\\sigma)$ a family of unbounded Fredholm operators $D\\subset H_1\\to H_2$ of index 0 depending smoothly on $(y,\\sigma)\\in \\Y\\times \\Sigma$ and holomorphically on $\\sigma$. We show how to associate to $\\scrP$, under mild hypotheses, a smooth vector bundle $\\kerb\\to\\Y$ whose fiber over a given $y\\in \\Y$ consists of classes, modulo holomorphic elements, of meromorphic elements $\\phi$ with $\\scrP_y\\phi$ holomorphic. As applications we give two examples relevant in the general theory of boundary value problems for elliptic wedge operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-24T15:17:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J32",
      "58J05",
      "35J48",
      "35J58"
    ],
    "keywords": [
      "holomorphic fredholm family",
      "kernel bundle",
      "boundary value problems",
      "smooth vector bundle",
      "elliptic wedge operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.5811K"
    }
  }
}