{
  "abstract": "We prove that the $(-2,3,7)$ pretzel knot is the only hyperbolic knot of genus at most $5$ with a lens space surgery. Our key technical result asserts that if a genus-$g$ hyperbolic knot $K$ has an elliptic surgery of slope greater than $4g-3$, then the invariant foliations of its monodromy have an orientation that is reversed by the monodromy, and so the opposite of the dilatation must be a root of the Alexander polynomial of $K$. Combined with prior work of Moser, Wu, Bleiler--Litherland, Baker, and Greene, this verifies the Berge conjecture for knots of genus at most $5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39260",
  "author_total": 2,
  "authors": [
    {
      "name": "Misha Schmalian"
    },
    {
      "name": "Steven Sivek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvk4hepe9rttf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39260",
  "fulltext_url": null,
  "id": "bvk4hepe9rttf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39260",
  "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": "W7215121093",
  "pdf_url": "https://arxiv.org/pdf/2609.39260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvk4hepe9rttf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lens space surgeries on knots of small genus",
  "title_text": "Lens space surgeries on knots of small genus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/bvk4hepe9rttf",
  "venue": "arXiv",
  "versions": []
}