{
  "id": "math/0405269",
  "version": "v1",
  "published": "2004-05-14T06:29:20.000Z",
  "updated": "2004-05-14T06:29:20.000Z",
  "title": "The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifolds",
  "authors": [
    "Suhyoung Choi"
  ],
  "comment": "27 pages, 10 figures",
  "journal": "Siberian Mathematical Journal vol. 47 (2006) 955-974",
  "doi": "10.1007/s11202-006-0107-5",
  "categories": [
    "math.GT"
  ],
  "abstract": "Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-manifold is decreasing and that summed with the cone angle squared is increasing as we deform the cone-angles. We confirm this near 0 cone-angles for an infinite family of hyperbolic cone-manifolds obtained by Dehn surgeries along the Whitehead link complements. The basic method is based on explicit holonomy computations using the A-polynomials and finding the maximal tubes. One of the key tool is the Taylor expression of a geometric component of the zero set of the A-polynomial in terms of the cone-angles. We also show a sequence of Taylor expressions for Dehn surgered manifolds converges to one for the limit hyperbolic manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-14T06:29:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "hyperbolic cone-manifolds",
      "maximal tubes",
      "deformations",
      "taylor expression",
      "maximal tubular neighborhoods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5269C"
    }
  }
}