{
  "id": "math/0502293",
  "version": "v2",
  "published": "2005-02-14T17:30:47.000Z",
  "updated": "2005-08-24T14:03:05.000Z",
  "title": "Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure",
  "authors": [
    "Dubravko Ivansic",
    "John G. Ratcliffe",
    "Steven T. Tschantz"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-41.abs.html",
  "journal": "Algebr. Geom. Topol. 5 (2005) 999-1026",
  "categories": [
    "math.GT"
  ],
  "abstract": "Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of some of those manifolds are then shown to be complements of tori and Klein bottles in other simply-connected closed 4-manifolds. All the examples are based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact hyperbolic 4-manifolds of minimal volume. Our examples are finite covers of some of those manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-08-24T14:03:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57Q45"
    ],
    "keywords": [
      "klein bottles",
      "hyperbolic structure",
      "noncompact hyperbolic",
      "finite covers",
      "topologically complements"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}