{
  "abstract": "We define a $d$-cube in a graph $G$ to be monophobic in $G$ if, whenever it supports a $d$-face of a discrete singular $d+1$-cube, it must also support another face. In many cases, the presence of such cubes implies the nontriviality of discrete cubical homology and homotopy groups associated with $G$. We describe several large classes of examples and characterize the property completely when $d=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14502",
  "author_total": 2,
  "authors": [
    {
      "name": "Curtis Greene"
    },
    {
      "name": "Samira Sahar Jamil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3k327bbq7qfwr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14502",
  "fulltext_url": null,
  "id": "3k327bbq7qfwr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14502",
  "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"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221807763",
  "pdf_url": "https://arxiv.org/pdf/2610.14502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3k327bbq7qfwr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Monophobic Neighborhoods of Cubes",
  "title_text": "Monophobic Neighborhoods of Cubes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3k327bbq7qfwr",
  "venue": "arXiv",
  "versions": []
}