{
  "id": "1809.01416",
  "version": "v1",
  "published": "2018-09-05T10:00:38.000Z",
  "updated": "2018-09-05T10:00:38.000Z",
  "title": "Dolbeault cohomology for almost complex manifolds",
  "authors": [
    "Joana Cirici",
    "Scott O. Wilson"
  ],
  "comment": "37 pages",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the Dolbeault cohomology, and develop a harmonic theory which injects into Dolbeault cohomology. Lie-theoretic analogues of the theory are developed which yield important calculational tools for Lie groups and nilmanifolds. Finally, we study applications to maximally non-integrable manifolds, including nearly K\\\"ahler $6$-manifolds, and show Dolbeault cohomology can be used to prohibit the existence of nearly K\\\"ahler metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-05T10:00:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex manifolds",
      "yield important calculational tools",
      "paper extends dolbeault cohomology",
      "harmonic theory",
      "study applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}