{
  "id": "math/0302318",
  "version": "v5",
  "published": "2003-02-25T20:44:18.000Z",
  "updated": "2003-12-14T15:49:22.000Z",
  "title": "Existence of foliations on 4-manifolds",
  "authors": [
    "Alexandru Scorpan"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-43.abs.html",
  "journal": "Algebr. Geom. Topol. 3 (2003) 1225-1256",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures on most 4-manifolds. In certain cases, one can prescribe surfaces to be transverse or be leaves of these foliations. The purpose of this paper is to offer objects, hoping for a future theory to be developed on them. For example, foliations that are taut might offer genus bounds for embedded surfaces (Kronheimer's conjecture).",
  "revisions": [
    {
      "version": "v5",
      "updated": "2003-12-14T15:49:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "57N13",
      "32Q60"
    ],
    "keywords": [
      "foliations",
      "offer genus bounds",
      "prescribe surfaces",
      "kronheimers conjecture",
      "existence results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}