{
  "id": "1903.10043",
  "version": "v1",
  "published": "2019-03-24T19:15:30.000Z",
  "updated": "2019-03-24T19:15:30.000Z",
  "title": "Almost complex manifolds are (almost) complex",
  "authors": [
    "Tobias Shin"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.AT",
    "math.CV",
    "math.SG"
  ],
  "abstract": "We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion relation by Demailly and Gaussier. We prove that the relation has formal solutions up to complex dimension 77, and that, given a formal solution, there is always a holonomic section approximating it. The latter result implies in particular that, up to complex dimension 77, any almost complex manifold admits a sequence of almost complex structures so that the pointwise supremum norms of the Nijenhuis tensors become arbitrarily small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-24T19:15:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex structures",
      "formal solution",
      "complex dimension",
      "complex manifold admits",
      "result implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}