{
  "id": "1910.03450",
  "version": "v1",
  "published": "2019-10-08T15:18:50.000Z",
  "updated": "2019-10-08T15:18:50.000Z",
  "title": "Vector fields and genus in dimension 3",
  "authors": [
    "Pierre Dehornoy",
    "Ana Rechtman"
  ],
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Given a flow on a 3-dimensional integral homology sphere, we give a formula for the Euler characteristic of its transverse surfaces, in terms of boundary data only. We illustrate the formula with several examples, in particular with surfaces of low genus. As an application, we show that for a right-handed flow with an ergodic invariant measure, the genus is an asymptotic invariant of order 2 proportional to the helicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-08T15:18:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector fields",
      "integral homology sphere",
      "ergodic invariant measure",
      "euler characteristic",
      "boundary data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}