{
  "id": "1305.4215",
  "version": "v2",
  "published": "2013-05-18T01:37:05.000Z",
  "updated": "2015-11-04T21:26:37.000Z",
  "title": "Homomorphims from the fundamental group of planar sets",
  "authors": [
    "Curt Kent"
  ],
  "comment": "This is a short note showing how to extend a previous paper by the author and Greg Conner to the planar setting",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We prove that every homomorphism from the fundamental group of a planar Peano continuum to the fundamental group of a planar or one-dimensional Peano continuum is induced by a continuous map up to conjugation. This is then used to provide a family of uncountable many planar Peano continua with pairwise non-isomorphic fundamental groups all of which are not homotopy equivalent to a one-dimensional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-18T01:37:05.000Z",
      "abstract": "We show that every homomorphism from the fundamental group of a planar Peano continuum to the fundamental group of a planar or one-dimensional Peano continuum is induced by a continuous map up to conjugation.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-04T21:26:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "planar sets",
      "homomorphims",
      "planar peano continuum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4215K"
    }
  }
}