{
  "id": "1709.09211",
  "version": "v1",
  "published": "2017-09-26T18:27:11.000Z",
  "updated": "2017-09-26T18:27:11.000Z",
  "title": "Homotopy type of planar continua",
  "authors": [
    "Curtis Kent"
  ],
  "comment": "18 pages. Comments welcome",
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to prove that two planar or one-dimensional Peano continua are homotopy equivalent if and only if they have isomorphic fundamental groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T18:27:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy type",
      "planar continua",
      "peano continuum",
      "isomorphic fundamental groups",
      "one-dimensional peano continua"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}