{
  "annotation_id": "1f4b27c3-f746-4d66-9fa4-cec681ae9a0e",
  "date_created": "2026-02-17T05:53:04.327000Z",
  "date_modified": "2026-02-17T05:53:04.327000Z",
  "file_hash": "39f015d54f9bd192ec65a843c02320a7ec0384b1540b60328fb28a5195470acc",
  "private": false,
  "record": {
    "abstract": "A reductive homogeneous space $G/H$ is always diffeomorphic to the normal bundle of an orbit of a maximal compact subgroup of $G$. We prove that if $G/H$ admits compact quotients, then the sphere bundle associated to this normal bundle is fiber-homotopically trivial. We deduce that many reductive homogeneous spaces do not admit compact quotients, such as the complex spheres $\\mathrm{O}(n+1,\\mathbb{C})/\\mathrm{O}(n,\\mathbb{C})$ for all $n \\notin \\{1,3,7\\}$, or $\\mathrm{SL}(n,\\mathbb{R})/\\mathrm{SL}(m,\\mathbb{R})$ for all $n\u003em\u003e1$, which solves conjectures of T. Kobayashi from the early 1990s. We also prove that if the pseudo-Riemannian hyperbolic space $\\mathbf{H}^{p,q}$ of signature $(p,q)$ admits compact quotients, then $p$ must be divisible by at least $2^{\\lfloor q/2\\rfloor}$.",
    "arxiv_id": "2601.05857",
    "authors": [
      "Fanny Kassel",
      "Yosuke Morita",
      "Nicolas Tholozan"
    ],
    "categories": [
      "math.GT",
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Compact quotients of homogeneous spaces and homotopy theory of sphere bundles",
    "url": "https://arxiv.org/abs/2601.05857",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c62fb1c9-6c3b-4b9d-8e90-8cff46a4ce0c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}