{
  "id": "2401.08000",
  "version": "v1",
  "published": "2024-01-15T22:58:37.000Z",
  "updated": "2024-01-15T22:58:37.000Z",
  "title": "Ultracoproducts and weak containment for flows of topological groups",
  "authors": [
    "Andy Zucker"
  ],
  "comment": "preliminary version; comments welcome",
  "categories": [
    "math.DS",
    "math.LO",
    "math.OA"
  ],
  "abstract": "We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups. For the class of locally Roelcke precompact groups, the theory is especially rich, allowing us to define for certain families of $G$-flows a suitable compact space of weak types. When $G$ is locally compact, all $G$-flows belong to one such family, yielding a single compact space describing all weak types of $G$-flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T22:58:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak containment",
      "ultracoproducts",
      "weak types",
      "locally roelcke precompact groups",
      "single compact space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}