{
  "abstract": "Motivated by the relative-slice problem in $4$-manifold topology, we define for a knot $R$ the notion of a relative knot concordance group $\\mathcal{C}_R$ and analyze the structure of its algebraic analogue $\\mathcal{AC}_R$ modulo torsion. Using Milnor signatures, we show that $\\mathcal{AC}_R$ has infinite rank for every $R$. We also show that any prescribed finite set of natural numbers can be realized as orders of elements in a single relative concordance group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19467",
  "author_total": 2,
  "authors": [
    {
      "name": "Vyacheslav Krushkal"
    },
    {
      "name": "Ryan Stees"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wsfcdvajgvyd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19467",
  "fulltext_url": null,
  "id": "3wsfcdvajgvyd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19467",
  "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"
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  ],
  "openalex": "W7222240394",
  "pdf_url": "https://arxiv.org/pdf/2610.19467",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wsfcdvajgvyd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19467",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19467"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Relative knot concordance",
  "title_text": "Relative knot concordance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/3wsfcdvajgvyd",
  "venue": "arXiv",
  "versions": []
}