{
  "id": "2004.07409",
  "version": "v1",
  "published": "2020-04-16T00:59:00.000Z",
  "updated": "2020-04-16T00:59:00.000Z",
  "title": "Dynamical obstructions for classification by actions of TSI groups",
  "authors": [
    "Shaun Allison",
    "Aristotelis Panagiotopoulos"
  ],
  "comment": "18 pages",
  "categories": [
    "math.LO",
    "math.AT",
    "math.DS",
    "math.OA"
  ],
  "abstract": "We introduce a dynamical condition for Polish $G$-spaces, in the spirit of Hjorth's turbulence theory, which implies non-classifiability by actions of Polish TSI-groups. These are the groups which admit a metric that is invariant from both sides. We show that the wreath product of any two non-compact subgroups of $S_{\\infty}$ admits an action whose orbit equivalence relation is generically ergodic against actions of TSI-groups, and deduce that there is an orbit equivalence relation of a CLI group which is not classifiable by TSI group actions. Finally, we show that Morita equivalence of continuous-trace $C^*$-algebras, as well as isomorphism of Hermitian line bundles, are not classifiable by TSI-group actions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-16T00:59:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H05",
      "37B02",
      "54H11",
      "46L35",
      "55R15"
    ],
    "keywords": [
      "dynamical obstructions",
      "orbit equivalence relation",
      "classification",
      "hermitian line bundles",
      "hjorths turbulence theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}