{
  "abstract": "In this paper we study a discrete homotopy theory for undirected graphs. More precisely, we consider $A$-homotopy groups, first defined in the work of Barcelo, Kramer, Laubenbacher and Weaver. For every degree $n$ and every group $G$ (Abelian if $n\\geq 2$), we construct a graph whose $n$-th $A$-homotopy group is isomorphic to $G$ and whose other $A$-homotopy groups all vanish. Using these, we show that for every infinite sequence of groups $G_1,G_2,\\ldots$, with $G_i$ Abelian for $i\\geq 2$, there is a graph $X$ such that the $i$-th $A$-homotopy group of $X$ is isomorphic to $G_i$ for all $i$. Along the way, we identify relative $A$-homotopy groups with relative classical homotopy groups, and prove a discrete version of the Blakers-Massey theorem. We then construct partial Postnikov systems and (full) Whitehead towers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03497",
  "author_total": 1,
  "authors": [
    {
      "name": "Georg Wille"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zgsza4zn1q1d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03497",
  "fulltext_url": null,
  "id": "9zgsza4zn1q1d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03497",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220450215",
  "pdf_url": "https://arxiv.org/pdf/2610.03497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zgsza4zn1q1d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Eilenberg-MacLane spaces in A-homotopy theory",
  "title_text": "Eilenberg-MacLane spaces in A-homotopy theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/9zgsza4zn1q1d",
  "venue": "arXiv",
  "versions": []
}