{
  "id": "1401.2621",
  "version": "v2",
  "published": "2014-01-12T13:01:05.000Z",
  "updated": "2015-01-26T16:18:16.000Z",
  "title": "Inverse monoids and immersions of 2-complexes",
  "authors": [
    "John Meakin",
    "Nóra Szakács"
  ],
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "It is well known that under mild conditions on a connected topological space $\\mathcal X$, connected covers of $\\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\\mathcal D} \\rightarrow \\mathcal C$ between CW-complexes is a cellular map such that each point $y \\in {\\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\\mathcal C$, we need to replace the fundamental group of $\\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-12T13:01:05.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-26T16:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M18",
      "57M20"
    ],
    "keywords": [
      "conjugacy classes",
      "fundamental group",
      "appropriate inverse monoid",
      "cw-complexes",
      "cellular map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}