{
  "abstract": "For split links the even Khovanov spectrum is a smash product of the spectra of the pieces; the odd one is not. For $T(2,m)\\sqcup T(2,n)$ we show that the odd spectrum is, in each quantum grading, a wedge of spheres and copies of a suspension of $\\mathbb{CP}^{2}$. Using the skein cofiber sequence at the level of spectra, we prove that for fixed $q-m-n$ the number of these copies is determined by finitely many small links and stabilizes for large $m$ and $n$. The $\\mathbb{CP}^{2}$ summand of $T(2,3)\\sqcup T(2,3)$, due to Schütz and Rajapakse, persists in quantum grading $m+n+8$ for all $m,n\\ge3$. We conjecture that the number of copies of $\\mathbb{CP}^{2}$ equals the number of copies of $\\mathbb{RP}^{2}\\wedge\\mathbb{RP}^{2}$ in the even spectrum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40245",
  "author_total": 1,
  "authors": [
    {
      "name": "Krishnendu Kar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99mnje560w8ka.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40245",
  "fulltext_url": null,
  "id": "99mnje560w8ka",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40245",
  "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.AT"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40245",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99mnje560w8ka.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40245",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40245"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Skein reduction and stabilization for the odd Khovanov spectra of $T(2,m)\\sqcup T(2,n)$",
  "title_text": "Skein reduction and stabilization for the odd Khovanov spectra of T(2,m)sqcup T(2,n)",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/99mnje560w8ka",
  "venue": "arXiv",
  "versions": []
}