{
  "id": "2004.12653",
  "version": "v1",
  "published": "2020-04-27T09:04:30.000Z",
  "updated": "2020-04-27T09:04:30.000Z",
  "title": "Iterated Monodromy Groups of Exponential Maps",
  "authors": [
    "Bernhard Reinke"
  ],
  "comment": "16 Pages, Comments welcome!",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an explicit construction in terms of kneading sequences. We investigate the group theoretic properties of these groups, and show in particular that they are amenable, but they are not elementary subexponentially amenable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-27T09:04:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37B10",
      "20E08"
    ],
    "keywords": [
      "iterated monodromy groups",
      "exponential maps",
      "group theoretic properties",
      "post-singularly finite exponential functions",
      "explicit construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}