{
  "id": "2111.06319",
  "version": "v1",
  "published": "2021-11-11T17:19:01.000Z",
  "updated": "2021-11-11T17:19:01.000Z",
  "title": "Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition",
  "authors": [
    "Colin Adams",
    "Michele Capovilla-Searle",
    "Darin Li",
    "Lily Qiao Li",
    "Jacob McErlean",
    "Alexander Simons",
    "Natalie Stewart",
    "Xiwen Wang"
  ],
  "comment": "45 pages, 19 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the appropriately defined hyperbolic volumes of the pieces. A variety of examples of appropriately hyperbolic pieces and volumes are provided, with many examples from link complements in the 3-sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-11T17:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K32"
    ],
    "keywords": [
      "lower bounds",
      "decomposition",
      "appropriately defined hyperbolic volumes",
      "appropriate type",
      "appropriately hyperbolic pieces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}