{
  "abstract": "Given a free group on $n$ generators, $F_n$, and a topological group $G$, $\\operatorname{Aut}\\left(F_n\\right)$ acts on $\\operatorname{Epi}\\left(F_n,G\\right)$, the set of homomorphisms $f:F_n \\rightarrow G$ with dense image. $f\\in \\operatorname{Epi}\\left(F_n,G\\right)$ is called redundant if there is a proper free factor $A < F_n$ whose image under $f$ is dense in $G$. For $n \\ge 3$, $G = \\operatorname{PSL}_2 \\left(\\mathbb{Q}_p\\right)$, we prove that every $f\\in \\operatorname{Epi}\\left(F_n,G\\right)$ with torsion-free image is redundant, and give sufficient conditions for $f$ to be redundant even when its image is not torsion-free.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37237",
  "author_total": 2,
  "authors": [
    {
      "name": "Yair Glasner"
    },
    {
      "name": "Amit Levinson-Sela"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8w4w25c7hkkgs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37237",
  "fulltext_url": null,
  "id": "8w4w25c7hkkgs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37237",
  "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"
    ]
  ],
  "openalex": "W7214964456",
  "pdf_url": "https://arxiv.org/pdf/2609.37237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8w4w25c7hkkgs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Redundant generation in $\\operatorname{PSL}_2\\left(\\mathbb{Q}_p\\right)$",
  "title_text": "Redundant generation in PSL_2(ℚ_p)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/8w4w25c7hkkgs",
  "venue": "arXiv",
  "versions": []
}