{
  "id": "2312.14255",
  "version": "v1",
  "published": "2023-12-21T19:13:13.000Z",
  "updated": "2023-12-21T19:13:13.000Z",
  "title": "Entropy versus volume via Heegaard diagrams",
  "authors": [
    "Yi Liu"
  ],
  "comment": "50 pages; comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "The following inequalities are established, improving a former inequality due to Kojima. For any closed arithmetic hyperbolic $3$--manifold fibering over a circle, the entropy of the pseudo-Anosov monodromy is bounded by the hyperbolic volume of the $3$--manifold, up to a universal constant factor. For any closed hyperbolic $3$--manifold fibering over a circle with systole $\\geq\\varepsilon>0$, the entropy is bounded by the hyperbolic volume times $\\log(3+1/\\varepsilon)$, up to a universal constant factor. The proof relies on Heegaard Floer homology and hyperbolic geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-21T19:13:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K32",
      "57K20",
      "57K18"
    ],
    "keywords": [
      "heegaard diagrams",
      "universal constant factor",
      "hyperbolic volume times",
      "heegaard floer homology",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}