{
  "id": "1703.03010",
  "version": "v1",
  "published": "2017-03-08T19:50:53.000Z",
  "updated": "2017-03-08T19:50:53.000Z",
  "title": "Extending group actions on metric spaces",
  "authors": [
    "C. Abbott",
    "D. Hume",
    "D. Osin"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We address the following natural extension problem for group actions: Given a group $G$, a subgroup $H\\le G$, and an action of $H$ on a metric space, when is it possible to extend it to an action of the whole group $G$ on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of $H$? We begin by formalizing this problem and present a construction of an induced action which behaves well when $H$ is hyperbolically embedded in $G$. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. We also obtain some results for elementary amenable groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-08T19:50:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric space",
      "extending group actions",
      "natural extension problem",
      "extension preserve interesting properties",
      "induced action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}