{
  "abstract": "We prove the Bleiler-Litherland conjecture: every lens space obtained by a nontrivial Dehn surgery on a hyperbolic knot in $S^3$ has order at least 18. The key ingredient is a spectral obstruction: if a hyperbolic knot $K$ of genus $g$ admits a lens space surgery with slope $\\pm(4g-2)$, then $Δ_K(t)$ has a real root outside the unit circle. The proof combines Floer-theoretic restrictions on lens space surgeries, Gabai's degeneracy-slope bound and Gabai-Oertel's persistence theorem for essential laminations, Ni's fixed-point theorem for monodromy, and a mod-2 orientability criterion, together with the relation between homological monodromy and the Alexander polynomial. As a further application of this spectral obstruction, we obtain characterizing-slope results for torus knots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31757",
  "author_total": 1,
  "authors": [
    {
      "name": "Qilong Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hd61stxtq7y6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31757",
  "fulltext_url": null,
  "id": "8hd61stxtq7y6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31757",
  "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": "W7214789950",
  "pdf_url": "https://arxiv.org/pdf/2609.31757",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hd61stxtq7y6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.31757",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31757"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lens Space Surgeries and the Bleiler-Litherland Conjecture",
  "title_text": "Lens Space Surgeries and the Bleiler-Litherland Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/8hd61stxtq7y6",
  "venue": "arXiv",
  "versions": []
}