{
  "abstract": "We establish new restrictions on the virtual cohomological dimension of word hyperbolic groups admitting Anosov representations into $\\operatorname{PO}(p, q)$ ($p > q \\geq 2$) or the exceptional Lie group $\\operatorname{G}_2'$. Our main result states that, if $P_k$ is the parabolic subgroup of $\\operatorname{PO}(p, q)$ stabilizing an isotropic $k$-plane in $\\mathbb{R}^{p, q}$, a group admitting a $\\{P_1,P_q\\}$-Anosov representation into $\\operatorname{PO}(p, q)$ has virtual cohomological dimension strictly less than $p$. As a result, a $\\mathbf{H}^{p, q-1}$-convex cocompact subgroup of $\\operatorname{PO}(p, q)$ cannot act properly discontinuously and cocompactly on $\\mathbf{H}^{p, q-1}$. The main theorem also implies that a group admitting a $P_α$-Anosov representation into the exceptional Lie group $\\operatorname{G}_2'$ has virtual cohomological dimension strictly less than $4$, where $α$ is a short restricted root of $\\operatorname{G}_2'$. As an application, we prove that the homogeneous space $\\operatorname{G}_2'/ \\operatorname{SU}(2, 1)$ does not admit any compact quotient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20197",
  "author_total": 1,
  "authors": [
    {
      "name": "Kewei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvdv59de28rrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20197",
  "fulltext_url": null,
  "id": "cvdv59de28rrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20197",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7222271022",
  "pdf_url": "https://arxiv.org/pdf/2610.20197",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvdv59de28rrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20197",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20197"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Topological obstruction for Anosov representations into $\\operatorname{PO}(p, q)$",
  "title_text": "Topological obstruction for Anosov representations into PO(p, q)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cvdv59de28rrz",
  "venue": "arXiv",
  "versions": []
}