{
  "id": "2406.02519",
  "version": "v1",
  "published": "2024-06-04T17:40:03.000Z",
  "updated": "2024-06-04T17:40:03.000Z",
  "title": "The space of immersed polygons",
  "authors": [
    "Maxime Fortier Bourque"
  ],
  "comment": "7 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We use the Schwarz--Christoffel formula to show that for every $n\\geq 3$, the space of labelled immersed $n$-gons in the plane up to similarity is homeomorphic to $\\mathbb{R}^{2n-4}$. It follows that the space of labelled simple $n$-gons up to similarity is homeomorphic to $\\mathbb{R}^{2n-4}$ if $n\\in \\{3,4,5\\}$, which confirms one more case of a conjecture of Gonz\\'alez and Sedano-Mendoza.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-04T17:40:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "immersed polygons",
      "homeomorphic",
      "schwarz-christoffel formula",
      "similarity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}