{
  "id": "1403.2071",
  "version": "v2",
  "published": "2014-03-09T16:18:56.000Z",
  "updated": "2015-05-19T17:09:51.000Z",
  "title": "A fast convergence theorem for nearly multiplicative connections on proper Lie groupoids",
  "authors": [
    "Giorgio Trentinaglia"
  ],
  "comment": "60 pages. In the new version, more general statements of the main theorems are given which do no longer rely on the assumption of source-properness. As a consequence, Appendix B has been expanded. Some minor changes have been introduced throughout, especially to the terminology. The introduction has been rewritten. Some references have been added",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "Motivated by the study of global geometric properties of differentiable stacks presented by proper Lie groupoids, we investigate the existence of multiplicative connections on such groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fact presented here relies on a recursive averaging technique. We regard our results as a preliminary step towards the construction of an obstruction theory for multiplicative connections on proper Lie groupoids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-09T16:18:56.000Z",
      "abstract": "Motivated by the study of global geometric properties of differentiable stacks associated with proper Lie groupoids we investigate the existence of multiplicative connections on such groupoids. Under mild technical assumptions (source properness) we show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fact presented here relies on a recursive averaging technique. We regard our results as an initial step towards the construction of an obstruction theory for multiplicative connections on proper Lie groupoids.",
      "comment": "56 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-19T17:09:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A22",
      "58H05",
      "53C05",
      "58C30"
    ],
    "keywords": [
      "proper lie groupoids",
      "multiplicative connection",
      "fast convergence theorem",
      "global geometric properties",
      "mild technical assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2071T"
    }
  }
}