{
  "abstract": "For any prime number $p$, the classic Hopkins-Mahowald theorem asserts that $H\\mathbb{Z}/p$ is an $\\mathbb{E}_2$-Thom spectrum over the $p$-complete sphere spectrum. Kitchloo extended this result to show that $H\\mathbb{Z}/p^k$ is an $\\mathbb{E}_2$-Thom spectrum over the $p$-local sphere spectrum, except for the case when $(p, k) = (2, 2)$. We solve the remaining case by showing that $H\\mathbb{Z}/4$ is not an $\\mathbb{E}_2$-Thom spectrum over the $2$-complete sphere spectrum, and consequently the $2$-local sphere spectrum. This work was developed with substantial assistance from GPT-5.6 Sol and GPT-6 Astra, and an early draft was subsequently reviewed using Claude Fable 5.1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19446",
  "author_total": 1,
  "authors": [
    {
      "name": "Mattie Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50n4hx1f67pa2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19446",
  "fulltext_url": null,
  "id": "50n4hx1f67pa2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19446",
  "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"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7213601382",
  "pdf_url": "https://arxiv.org/pdf/2609.19446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50n4hx1f67pa2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19446"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$H\\mathbb{Z}/4$ is not an $\\mathbb{E}_2$-Thom Spectrum over the $2$-Complete Sphere Spectrum",
  "title_text": "Hℤ/4 is not an 𝔼_2-Thom Spectrum over the $2$-Complete Sphere Spectrum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/50n4hx1f67pa2",
  "venue": "arXiv",
  "versions": []
}