{
  "id": "2409.14504",
  "version": "v1",
  "published": "2024-09-22T16:03:50.000Z",
  "updated": "2024-09-22T16:03:50.000Z",
  "title": "On the Euler class one conjecture for fillable contact structures",
  "authors": [
    "Yi Liu"
  ],
  "comment": "20 pages; comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, it is proved that every oriented closed hyperbolic $3$--manifold $N$ admits some finite cover $M$ with the following property. There exists some even lattice point $w$ on the boundary of the dual Thurston norm unit ball of $M$, such that $w$ is not the real Euler class of any weakly symplectically fillable contact structure on $M$. In particular, $w$ is not the real Euler class of any transversely oriented, taut foliation on $M$. This supplies new counter-examples to Thurston's Euler class one conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-22T16:03:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K32",
      "57K18",
      "57K33"
    ],
    "keywords": [
      "real euler class",
      "symplectically fillable contact structure",
      "conjecture",
      "dual thurston norm unit ball",
      "thurstons euler class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}