{
  "id": "math/0603069",
  "version": "v1",
  "published": "2006-03-03T05:48:47.000Z",
  "updated": "2006-03-03T05:48:47.000Z",
  "title": "The homotopy dimension of codiscrete subsets of the 2-sphere",
  "authors": [
    "J. W. Cannon",
    "G. R. Conner"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopically 1-dimensional, we prove that each has fundamental group that embeds in the fundamental group of a 1-dimensional planar Peano continuum. We leave open the following question: Is a planar Peano continuum homotopically 1- dimensional if its fundamental group is isomorphic with the fundamental group of a 1-dimensional planar Peano continuum?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-03T05:48:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F50",
      "55M10"
    ],
    "keywords": [
      "fundamental group",
      "codiscrete subsets",
      "homotopy dimension",
      "homotopy equivalent",
      "leave open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3069C"
    }
  }
}