{
  "id": "1201.0791",
  "version": "v1",
  "published": "2012-01-04T00:28:31.000Z",
  "updated": "2012-01-04T00:28:31.000Z",
  "title": "On the local and global classification of generalized complex structures",
  "authors": [
    "Michael Bailey"
  ],
  "comment": "112 pages, thesis",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a complex point arises from a holomorphic Poisson structure. In the proof we use a smoothed Newton's method along the lines of Nash, Moser and Conn. In the second topic, we consider whether a given regular Poisson structure and transverse complex structure come from a generalized complex structure. We give cohomological criteria, and we find some counterexamples and some unexpected examples, including a compact, regular generalized complex manifold for which nearby symplectic leaves are not symplectomorphic. In the third topic, we consider generalized complex structures with nondegenerate type change; we describe a generalized Calabi-Yau structure induced on the type change locus, and prove a local normal form theorem near this locus. Finally, in the fourth topic, we give a classification of generalized complex principal bundles satisfying a certain transversality condition; in this case, there is a generalized flat connection, and the classification involves a monodromy map to the Courant automorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-04T00:28:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D18"
    ],
    "keywords": [
      "generalized complex structure",
      "global classification",
      "complex principal bundles satisfying",
      "generalized complex manifold",
      "transverse complex structure come"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 112,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.0791B"
    }
  }
}