{
  "abstract": "Let $n \\geq 4$ and $ρ: π_1S \\rightarrow PSL(n,\\mathbb{R})$ be a Hitchin representation. We study the topology of a cocompact domain of discontinuity $Ω_ρ$ in the flag manifold $\\mathcal{F}_{1,n-1}$ of line-hyperplane pairs in $\\mathbb{R}^n$ defined by Guichard-Wienhard. In particular, we lift $Ω$ to its $(\\mathbb{Z}_2\\times \\mathbb{Z}_2)$-cover $\\hatΩ$ in the Stiefel manifold $V_2(\\mathbb{R}^n)$. The domain $\\hatΩ$ is highly connected and smoothly fibers over hyperbolic space $\\mathbb{H}^2$ with unknown fiber $\\hat{\\mathfrak{F}}$, a closed $(2n-5)$-manifold. We determine the homeomorphism type of $\\hat{\\mathfrak{F}}$ as well as its diffeomorphism type up to connected sum with a homotopy sphere. The classification of $\\hat{\\mathfrak{F}}$ involves computing both its homology and a certain differential topology invariant needed to invoke Wall's classification of highly connected odd-dimensional manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31567",
  "author_total": 2,
  "authors": [
    {
      "name": "Parker Evans"
    },
    {
      "name": "Andrea Tamburelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51j9pdkyjynek.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31567",
  "fulltext_url": null,
  "id": "51j9pdkyjynek",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31567",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214591316",
  "pdf_url": "https://arxiv.org/pdf/2609.31567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51j9pdkyjynek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Line-Hyperplane Structures for Hitchin Representations",
  "title_text": "On Line-Hyperplane Structures for Hitchin Representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/51j9pdkyjynek",
  "venue": "arXiv",
  "versions": []
}