{
  "abstract": "It has been of particular interest in recent years to relate categorifications of quantum knot invariants like the Jones polynomial to Floer-theoretic invariants like knot Floer homology using spectral sequences. In pursuit of Rasmussen's conjecture, Dowlin constructed a family of invariants with properties like those of Khovanov and Rozansky's $\\mathfrak{sl}_n$-homology theories. In this paper, we explore these invariants for $L$-space knots and thin knots. In particular, for $n\\geq 2$ the invariants of thin knots can be computed from a change of coefficients from the minus flavor of knot Floer homology, and the same holds for an $L$-space knot exactly when an explicit condition relating $n$ to its Alexander polynomial is satisfied.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38927",
  "author_total": 1,
  "authors": [
    {
      "name": "Tristan Wells"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38j9hys72t9tw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38927",
  "fulltext_url": null,
  "id": "38j9hys72t9tw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38927",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38j9hys72t9tw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38927"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$L$-Space Knots in $\\mathfrak{sl}_{n}$-like Knot Floer Homology",
  "title_text": "L-Space Knots in sl_n-like Knot Floer Homology",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/38j9hys72t9tw",
  "venue": "arXiv",
  "versions": []
}