{
  "abstract": "For every fixed integer $d\\geq2$, we prove that the finite graphs receiving a continuous homomorphism from the standard Schreier graph $F(2^{\\mathbb Z^d})$ form a $Σ^0_1$-complete set. This extends a theorem of Gao, Jackson, Krohne and Seward when $d=2$. For the positive part of the reduction, we show that if a graph $H$ satisfies a certain property then there is a continuous graph homomorphism from $F(2^{\\mathbb Z^d})$ to $H$, in particular, the complete graph $K_4$ satisfies this property. This extends a theorem of Gao and Jackson. We also prove that $\\big (\\mathcal H_d\\big )$ is a strictly decreasing sequence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39824",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruijun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cead902rsbc1r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39824",
  "fulltext_url": null,
  "id": "cead902rsbc1r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39824",
  "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.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7215091032",
  "pdf_url": "https://arxiv.org/pdf/2609.39824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cead902rsbc1r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Continuous graph homomorphisms of higher dimensional abelian group actions",
  "title_text": "Continuous graph homomorphisms of higher dimensional abelian group actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/cead902rsbc1r",
  "venue": "arXiv",
  "versions": []
}