{
  "abstract": "We prove that $S^1$, ${\\rm SU}(2)$, and ${\\rm SO}(3)$ are compact amalgamation bases: for each of these groups, any two compact groups with specified embedded copies of it embed in a compact group in which those copies agree. For compact Lie groups, the amalgam can be chosen to be a finite-dimensional unitary group. This research was conducted with substantial AI assistance, including in the development of mathematical constructions and proof arguments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27820",
  "author_total": 1,
  "authors": [
    {
      "name": "Andreas Thom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80c9w30v1pjt2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27820",
  "fulltext_url": null,
  "id": "80c9w30v1pjt2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27820",
  "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.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  ],
  "openalex": "W7214170363",
  "pdf_url": "https://arxiv.org/pdf/2609.27820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80c9w30v1pjt2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.27820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bergman's amalgamation problem over the circle",
  "title_text": "Bergman's amalgamation problem over the circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/80c9w30v1pjt2",
  "venue": "arXiv",
  "versions": []
}