{
  "id": "1910.11728",
  "version": "v1",
  "published": "2019-10-25T13:50:01.000Z",
  "updated": "2019-10-25T13:50:01.000Z",
  "title": "The realization and classification of topologically transitive group actions on $1$-manifolds",
  "authors": [
    "Enhui Shi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this report, we first recall the Poincar\\'e's classification theorem for minimal orientation-preserving homeomorphisms on the circle and the Ghys' classification theorem for minimal orientation-preserving group actions on the circle. Then we introduce a classification theorem for a specified class of topologically transitive orientation-preserving group actions on the circle by $\\mathbb Z^d$. Also, some groups that admit/admit no topologically transitive actions on the line are determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-25T13:50:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topologically transitive group actions",
      "transitive orientation-preserving group actions",
      "realization",
      "poincares classification theorem",
      "minimal orientation-preserving group actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}