{
  "abstract": "Given a topological space $X$ and a family of subgroups $\\mathcal{F}$ of $π_1(X)$, the $\\mathcal{F}$-category of $X$ is given as one less than the cardinality of the smallest cover of $X$ by open subsets whose fundamental groups lie in $\\mathcal{F}$. In this article we study $\\mathcal{F}$-categories of aspherical spaces and obtain cohomological lower bounds, a maximality result and bounded cohomology classes whose vanishing properties are crucial for determining $\\mathcal{F}$-categories. For this purpose, we study the bounded Adamson cohomology of a family of subgroups and discuss universality properties of bounded cohomology classes. We apply our techniques to derive some applications to the study of the monotonicity of $\\mathcal{F}$-categories under degree-one maps between manifolds and to provide a counterexample to a question of Capovilla, Löh and Moraschini.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07932",
  "author_total": 2,
  "authors": [
    {
      "name": "Arturo Espinosa Baro"
    },
    {
      "name": "Stephan Mescher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3h8za5erd0k3z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07932",
  "fulltext_url": null,
  "id": "3h8za5erd0k3z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07932",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221016892",
  "pdf_url": "https://arxiv.org/pdf/2610.07932",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3h8za5erd0k3z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07932",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07932"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On open covers of aspherical spaces satisfying $π_1$-constraints and bounded Adamson cohomology",
  "title_text": "On open covers of aspherical spaces satisfying π_1-constraints and bounded Adamson cohomology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/3h8za5erd0k3z",
  "venue": "arXiv",
  "versions": []
}