{
  "abstract": "In this paper, we give complete classifications of the finite groups $G$ for which the constant Eilenberg--Mac Lane spectra $H\\underline{\\mathbb Z}$ and $H\\underline{\\mathbb F}_2$ are Anderson self-dual up to a virtual representation shift, and we determine all such shifts. For both of these spectra, we determine the representation periodicity lattice for every finite group. As applications, we obtain $RO(G)$-graded universal coefficient theorems relating equivariant homology and cohomology, together with formulas for the Anderson duals of $H\\underline{\\mathbb Z}$-modules. In the $H\\underline{\\mathbb F}_2$ self-dual cases, we identify the graded $\\mathbb F_2$-linear dual of the coefficient ring $π_\\star^G H\\underline{\\mathbb F}_2$ with a representation shift of the ring as a module over itself. This gives perfect multiplication pairings and graded self-injectivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35796",
  "author_total": 5,
  "authors": [
    {
      "name": "Hana Jia Kong"
    },
    {
      "name": "Achim Krause"
    },
    {
      "name": "Yutao Liu"
    },
    {
      "name": "XiaoLin Danny Shi"
    },
    {
      "name": "Zhouli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxbacnm6a6t78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35796",
  "fulltext_url": null,
  "id": "dxbacnm6a6t78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35796",
  "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": "W7223994222",
  "pdf_url": "https://arxiv.org/pdf/2610.35796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxbacnm6a6t78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Anderson Dual of $H\\underline{\\mathbb Z}$ and $H\\underline{\\mathbb F}_2$",
  "title_text": "On the Anderson Dual of Hunderlineℤ and Hunderline𝔽_2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/dxbacnm6a6t78",
  "venue": "arXiv",
  "versions": []
}