{
  "abstract": "Suppose that a discrete group $G$ acts smoothly, properly, and effectively on a connected smooth manifold $M$, and let $q:M\\to M/G$ be the quotient map. We prove that if $q$ admits a continuous section, then $G$ is generated by reflections. We also establish converse results for dissecting reflections and give applications to Euclidean and lattice actions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26452",
  "author_total": 2,
  "authors": [
    {
      "name": "Suyoung Choi"
    },
    {
      "name": "Tao Gong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3th6nkcdqqvk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26452",
  "fulltext_url": null,
  "id": "a3th6nkcdqqvk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26452",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214122916",
  "pdf_url": "https://arxiv.org/pdf/2609.26452",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3th6nkcdqqvk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26452",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26452"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Sections of Quotient maps by Isometries",
  "title_text": "On Sections of Quotient maps by Isometries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/a3th6nkcdqqvk",
  "venue": "arXiv",
  "versions": []
}