{
  "id": "1908.03016",
  "version": "v1",
  "published": "2019-08-08T11:08:31.000Z",
  "updated": "2019-08-08T11:08:31.000Z",
  "title": "On the Anti-Invariant Cohomology of Almost Complex Manifolds",
  "authors": [
    "Richard Hind",
    "Adriano Tomassini"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the space of closed anti-invariant forms on an almost complex manifold, possibly non compact. We construct families of (non integrable) almost complex structures on $\\mathbb{R}^4$, such that the space of harmonic $J$-anti-invariant forms is infinite dimensional respectively $1$-dimensional. In the compact case, we construct $6$-dimensional almost complex manifolds with arbitrary large anti-invariant cohomology and a $2$-parameter family of almost complex strcuctures on the Kodaira-Thurston manifold whose anti-invariant cohomology group has maximum dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-08T11:08:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex manifold",
      "arbitrary large anti-invariant cohomology",
      "anti-invariant cohomology group",
      "construct families",
      "maximum dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}