{
  "abstract": "Let $\\mathcal{A}_0$ be the set of finitely generated free groups on some countable alphabet and and define $\\mathcal{A}_r$ inductively as the union of $\\mathcal{A}_{r-1}$ with the set of amalgamated free products $G_1\\ast_{\\ZZ}G_2$, where $G_1,G_2\\in \\mathcal{A}_{r-1}$. We show, for all $r$, that every element of $\\mathcal{A}_r$ has linear conjugator length, quantifying a result of Larsen and extending a result of Kharlampovich and Myasnikov. This is achieved by a linear conjugator length bound on a family of iterated HNN extensions of free groups. Also, in an appendix, we adapt a proof of A. Wei$ß$ to show that all Generalized Baumslag-Solitar Groups have linear conjugator length. As a consequence, we obtain that one-relator groups with non-trivial center have linear conjugator length, giving evidence for a conjecture of Bridson, Riley, and Sale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21116",
  "author_total": 1,
  "authors": [
    {
      "name": "Conan Gillis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj9sb4s8wf4bn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21116",
  "fulltext_url": null,
  "id": "dj9sb4s8wf4bn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21116",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213943021",
  "pdf_url": "https://arxiv.org/pdf/2609.21116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj9sb4s8wf4bn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.21116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Conjugator Length in Iterated Cyclic Amalgams of Free Groups",
  "title_text": "Conjugator Length in Iterated Cyclic Amalgams of Free Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dj9sb4s8wf4bn",
  "venue": "arXiv",
  "versions": []
}