{
  "id": "1103.1407",
  "version": "v1",
  "published": "2011-03-08T00:48:49.000Z",
  "updated": "2011-03-08T00:48:49.000Z",
  "title": "Locally compact subgroup actions on topological groups",
  "authors": [
    "Sergey A. Antonyan"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GN",
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $X$ be a Hausdorff topological group and $G$ a locally compact subgroup of $X$. We show that $X$ admits a locally finite $\\sigma$-discrete $G$-functionally open cover each member of which is $G$-homeomorphic to a twisted product $G\\times_H S_i$, where $H$ is a compact large subgroup of $G$ (i.e., the quotient $G/H$ is a manifold). If, in addition, the space of connected components of $G$ is compact and $X$ is normal, then $X$ itself is $G$-homeomorphic to a twisted product $G\\times_KS$, where $K$ is a maximal compact subgroup of $G$. This implies that $X$ is $K$-homeomorphic to the product $G/K\\times S$, and in particular, $X$ is homeomorphic to the product $\\Bbb R^n\\times S$, where $n={\\rm dim\\,} G/K$. Using these results we prove the inequality $ {\\rm dim}\\, X\\le {\\rm dim}\\, X/G + {\\rm dim}\\, G$ for every Hausdorff topological group $X$ and a locally compact subgroup $G$ of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-08T00:48:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "22F05",
      "54H11",
      "54H15",
      "54F45"
    ],
    "keywords": [
      "locally compact subgroup actions",
      "hausdorff topological group",
      "homeomorphic",
      "compact large subgroup",
      "maximal compact subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1407A"
    }
  }
}