{
  "abstract": "In this paper, we study height 4 knots, which generalize L-space knots and almost L-space knots studied by Ozsváth--Szabó, Baldwin--Sivek, and Binns. A knot $K\\subset S^3$ is called a height $m$ knot if $\\operatorname{rank} \\widehat{HF}(S^3_n(K))-n=m$ for all integers $n\\geq 2g(K)-1$, where $\\widehat{HF}$ is the hat version of Heegaard Floer homology introduced by Ozsváth--Szabó. In particular, height 0 and height 2 knots are exactly L-space knots and almost L-space knots, respectively. We prove that the knot Floer complex $CFK^\\infty(S^3,K)$ of a height 4 knot $K$ admits a basis that is horizontally and vertically simplified--an hv-basis for short. Moreover, we show that under such an hv-basis, the horizontal and vertical differentials fall into six cases, generalizing the results for L-space knots and almost L-space knots. The hv-basis of the knot Floer complex of $K$ can determine, via an explicit algorithm, the immersed curve of Hanselman-Rasmussen-Watson for the knot complement of $K$. Consequently, our results facilitate further exploration of computations of $\\widehat{HF}$ for the gluing of two height 4 knot complements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35305",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengyu Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qq25r12qydcq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35305",
  "fulltext_url": null,
  "id": "7qq25r12qydcq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35305",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223790031",
  "pdf_url": "https://arxiv.org/pdf/2610.35305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qq25r12qydcq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Knot Floer complexes of generalized L-space knots",
  "title_text": "Knot Floer complexes of generalized L-space knots",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7qq25r12qydcq",
  "venue": "arXiv",
  "versions": []
}