{
  "id": "1605.04365",
  "version": "v1",
  "published": "2016-05-14T01:58:40.000Z",
  "updated": "2016-05-14T01:58:40.000Z",
  "title": "Cartan connections on Lie algebroids and their integrability",
  "authors": [
    "Anthony D. Blaom"
  ],
  "comment": "29 pages, 9 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "A multiplicatively closed, horizontal $n$-plane field $D$ on a Lie groupoid $G$ over $M$ generalizes to \"intransitive geometry\" the classical notion of a Cartan connection. The infinitesimalization of the connection $D$ is a Cartan connection $\\nabla $ on the Lie algebroid of $G$, a notion already studied elsewhere by the author. It is shown that $\\nabla $ may be regarded as infinitesimal parallel translation in the groupoid $G$ along $D$. From this follows a proof that $D$ defines a \"pseudoaction\" generating a pseudogroup of transformations on $M$ precisely when the curvature of $\\nabla $ vanishes. A byproduct of this analysis is a detailed description of multiplication in the groupoid $J^1 G$ of one-jets of bisections of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-14T01:58:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "58H05"
    ],
    "keywords": [
      "cartan connection",
      "lie algebroid",
      "integrability",
      "infinitesimal parallel translation",
      "lie groupoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}