{
  "abstract": "Inspired by work in Seiberg--Witten and Heegaard Floer homology, Dunfield, Schütz, and the author constructed an abelian \"local equivalence group\" built from pairs of chain complexes, and a homomorphism from the smooth concordance group to this group that uses the odd Khovanov complex and the Bar-Natan deformation of the even Khovanov complex. Lewark independently gave a related local equivalence group and concordance invariant, using only the Bar-Natan deformation. In this paper, we construct $(\\mathbb{Z}/2\\mathbb{Z})^\\infty$ subgroups of Lewark's local equivalence group and the kernel of the map from our local equivalence group to Lewark's, as well as $\\mathbb{Z}^\\infty$ direct summands of Lewark's group and this kernel, invisible to the $s$-invariants. The construction gives at least six $\\mathbb{Z}$-valued concordance homomorphisms linearly independent from $s$, $τ$, and Dai--Hom--Stoffregen--Truong's invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37595",
  "author_total": 1,
  "authors": [
    {
      "name": "Robert Lipshitz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1edkxnx8jh48s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37595",
  "fulltext_url": null,
  "id": "1edkxnx8jh48s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37595",
  "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": "W7224115780",
  "pdf_url": "https://arxiv.org/pdf/2610.37595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1edkxnx8jh48s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Khovanov local equivalence groups",
  "title_text": "On Khovanov local equivalence groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1edkxnx8jh48s",
  "venue": "arXiv",
  "versions": []
}