{
  "abstract": "In 1974, E. M. Brown introduced the $\\wp$-functor to study the proper homotopy groups of an end, suggesting a parallel proper homology theory that has since remained undeveloped. In this paper, we construct this missing proper homology and relate it to proper homotopy by developing a proper Hurewicz theorem. Bypassing abstract pro-categorical machinery, we show that $\\wp$ has major advantages over the classical limits $\\varprojlim$ and $\\varprojlim^1$: it is exact, detects pro-triviality, satisfies a cardinality dichotomy, and connects to these classical limits through a 4-term exact sequence. As an application, we prove that the Brown--Grossman proper fundamental group of any open contractible $3$-manifold other than $\\mathbb{R}^3$ is uncountable and perfect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14063",
  "author_total": 2,
  "authors": [
    {
      "name": "Sumanta Das"
    },
    {
      "name": "Rekha Santhanam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb5vdgvexhzv5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14063",
  "fulltext_url": null,
  "id": "fb5vdgvexhzv5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14063",
  "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.GT"
    ],
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7213281014",
  "pdf_url": "https://arxiv.org/pdf/2609.14063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fb5vdgvexhzv5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Brown's Asymptotic Limit Functor and Proper Homology",
  "title_text": "Brown's Asymptotic Limit Functor and Proper Homology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fb5vdgvexhzv5",
  "venue": "arXiv",
  "versions": []
}