{
  "id": "2506.19098",
  "version": "v1",
  "published": "2025-06-23T20:20:21.000Z",
  "updated": "2025-06-23T20:20:21.000Z",
  "title": "Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds",
  "authors": [
    "Dmitry V. Bolotov"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2212.06807",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation $\\mathcal{F}$ of dimension one defined on a closed three-dimensional orientable manifold $M^3$ of negative curvature, which depends on the constants bounded the injectivity radius $inj(M^3)$, the volume $Vol(M^3)$, sectional curvature of the manifold $M^3$ and the mean curvature modulus of the leaves of the foliation $\\mathcal{F}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-23T20:20:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dual thurston norm",
      "euler class",
      "negative curvature",
      "arbitrary smooth foliation",
      "upper bound estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}