{
  "abstract": "We develop bar cohomology of link complements as an invariant of links in homology spheres. In this setting, bar cohomology is a Hopf algebra which is calculable using surfaces and their intersection curves in a link complement. In this first in a sequence of works, we introduce the invariant and show that it defines a canonical subspace of the tensor Hopf algebra, which already encodes information about Milnor's link invariants and provides geometrically significant information beyond them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11009",
  "author_total": 5,
  "authors": [
    {
      "name": "Greg Friedman"
    },
    {
      "name": "Nir Gadish"
    },
    {
      "name": "Robin Koytcheff"
    },
    {
      "name": "Dev Sinha"
    },
    {
      "name": "Ben Walter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dkbpdwhjevye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11009",
  "fulltext_url": null,
  "id": "3dkbpdwhjevye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11009",
  "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.AT"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7212315013",
  "pdf_url": "https://arxiv.org/pdf/2609.11009",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dkbpdwhjevye.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.11009",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11009"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Bar cohomology of links: beyond Milnor invariants",
  "title_text": "Bar cohomology of links: beyond Milnor invariants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/3dkbpdwhjevye",
  "venue": "arXiv",
  "versions": []
}