{
  "id": "1412.1304",
  "version": "v1",
  "published": "2014-12-03T12:52:57.000Z",
  "updated": "2014-12-03T12:52:57.000Z",
  "title": "Conjugacy classes of reflections of maps",
  "authors": [
    "Gareth A. Jones"
  ],
  "comment": "25 pages, 11 figures. Based on a talk presented at a conference on Graph Embeddings, St Petersburg, November 2014",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper considers how many conjugacy classes of reflections a map can have, under various transitivity conditions. It is shown that for vertex- and for face-transitive maps there is no restriction on their number or size, whereas edge-transitive maps can have at most four classes of reflections. Examples are constructed, using topology, covering spaces and group theory, to show that various distributions of reflections can be achieved. Connections with real forms of algebraic curves are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-03T12:52:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "14H37",
      "14H57",
      "20B25",
      "30F10",
      "30F50"
    ],
    "keywords": [
      "conjugacy classes",
      "reflections",
      "transitivity conditions",
      "group theory",
      "real forms"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.1304J"
    }
  }
}