{
  "id": "2411.11492",
  "version": "v1",
  "published": "2024-11-18T11:53:55.000Z",
  "updated": "2024-11-18T11:53:55.000Z",
  "title": "A criterion for virtual Euler class one",
  "authors": [
    "Yi Liu"
  ],
  "comment": "18 pages; comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M$ be an oriented closed hyperbolic $3$--manifold. Suppose that $w$ is a rational second cohomology class of $M$ with dual Thurston norm $1$. Upon the existence of certain nonvanishing Alexander polynomials, the author shows that the pullback of $w$ to some finite cover of $M$ is the real Euler class of some transversely oriented taut foliation on that cover. As application, the author constructs examples with first Betti number either $2$ or $3$, and partial examples with any first Betti number at least $4$, supporting Yazdi's virtual Euler class one conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-18T11:53:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "57R20",
      "57K31"
    ],
    "keywords": [
      "first betti number",
      "supporting yazdis virtual euler class",
      "rational second cohomology class",
      "real euler class",
      "dual thurston norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}