{
  "abstract": "In this paper, we establish several nonvanishing results for Floer lasagna modules $\\mathcal{FL}(W,K)$ for a smooth compact connected oriented $4$-manifold $W$ and a knot $K\\subset \\partial W$, via the evaluation maps to link Floer homology. We first establish a general criterion: if a certain Heegaard Floer cobordism map associated with a smooth $4$-manifold $W$ is nonzero, then $\\mathcal{FL}(W,U)\\neq 0$, where $U\\subset \\partial W$ is a local unknot. Applications include the nonvanishing of Floer lasagna modules for $\\#^m\\overline{\\mathbb{C}P^2}$ and for knot traces $X_n(K)$ when $K$ is slice and $n$ is a non-positive integer. In another direction, we show that for every nontrivial knot $K$ and every integer $n$, the Floer lasagna module $\\mathcal{FL}(X_n(K),K_n)$ is nonzero, where $K_n\\subset S_n^3(K)$ is the dual knot. Moreover, if $K$ is an L-space knot, then $\\mathcal{FL}(X_n(K),K_n)$ is infinite-dimensional for all integers $n\\ge \\max\\{2g(K),1\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00830",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5923agc38r1qt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00830",
  "fulltext_url": null,
  "id": "5923agc38r1qt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00830",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00830",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5923agc38r1qt.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00830",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00830"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the nonvanishing of Floer lasagna modules",
  "title_text": "On the nonvanishing of Floer lasagna modules",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5923agc38r1qt",
  "venue": "arXiv",
  "versions": []
}