{
  "abstract": "In this paper we study the multiplicity of contractible closed Reeb orbits on prequantization circle bundles. Building on the existing multiplicity result Theorem 1.3 for closed Reeb orbits on prequantization $S^1$-bundles, we weaken the index assumptions by requiring only that the supporting contact form has no contractible periodic Reeb orbits with mean Conley-Zehnder index zero and no contractible good periodic Reeb orbits with Conley-Zehnder index 0, and we obtain a lower bound for the number of geometrically distinct contractible closed Reeb orbits carried by contact forms $α$ on a prequantization $S^1$-bundle under certain natural topological assumptions (Theorem 1.6). In dimension five we further relax the index assumptions and show that, under a mild index condition imposed only on simple contractible periodic orbits and the same topological assumptions on the prequantization $S^1$-bundle, every non-degenerate supporting contact form carries at least $\\dim H_*(B;\\mathbb{Q})$ geometrically distinct contractible closed Reeb orbits (Theorem 1.11), in agreement with the conjectural lower bound for prequantization bundles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24557",
  "author_total": 2,
  "authors": [
    {
      "name": "Peng Liu"
    },
    {
      "name": "Dong Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frxgkp7hje4gt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24557",
  "fulltext_url": null,
  "id": "frxgkp7hje4gt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24557",
  "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.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223020244",
  "pdf_url": "https://arxiv.org/pdf/2610.24557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frxgkp7hje4gt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.24557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions",
  "title_text": "Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/frxgkp7hje4gt",
  "venue": "arXiv",
  "versions": []
}