{
  "id": "1101.5705",
  "version": "v1",
  "published": "2011-01-29T16:14:35.000Z",
  "updated": "2011-01-29T16:14:35.000Z",
  "title": "Connected components of definable groups and o-minimality I",
  "authors": [
    "Annalisa Conversano",
    "Anand Pillay"
  ],
  "comment": "26 pages. This paper corrects the paper \"Groups definable in o-minimal structures: structure theorem, G^000, definable amenability, and bounded orbits\" by the first author which was posted in December (1012.4540v1) and later withdrawn",
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a \"bounded orbit\" iff G is definably amenable. These results answer questions of Gismatullin, Newelski, Petrykovski. The examples also give new non G-compact first order theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-29T16:14:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "22F99"
    ],
    "keywords": [
      "definable groups",
      "connected components",
      "non g-compact first order theories",
      "o-minimality",
      "results answer questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}