{
  "id": "2207.12946",
  "version": "v1",
  "published": "2022-07-26T14:51:18.000Z",
  "updated": "2022-07-26T14:51:18.000Z",
  "title": "Topology of almost complex structures on six-manifolds",
  "authors": [
    "Gustavo Granja",
    "Aleksandar Milivojevic"
  ],
  "comment": "20 pages, comments very welcome",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-26T14:51:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q60",
      "53C27",
      "53C28",
      "55P62"
    ],
    "keywords": [
      "complex structures",
      "six-manifold",
      "rational homotopy theoretic minimal model",
      "twistor space",
      "vanishing first betti number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}