{
  "abstract": "This paper introduces relative versions of the inner automorphism group and the transvection group associated with surjective quandle homomorphisms. By using the relative inner automorphism group, we define a notion of connectedness for surjective homomorphisms. We characterize connected homomorphisms algebraically as quotient maps, and use the relative transvection group to establish a maximal connected--covering factorization for arbitrary surjections. We also introduce strongly connected homomorphisms via the relative transvection group, and classify them in terms of perfect normal subgroups of inner automorphism groups. A later part of this paper studies surjective homomorphisms for which the relative inner automorphism group acts $2$-transitively on each fiber. Under this assumption, we classify the possible quandle structures of the finite fibers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.02204",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuki Imamura"
    },
    {
      "name": "Tomoki Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/748q46vapdxvj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02204",
  "fulltext_url": null,
  "id": "748q46vapdxvj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02204",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7167224523",
  "pdf_url": "https://arxiv.org/pdf/2607.02204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/748q46vapdxvj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.02204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Relativization of symmetries on quandles",
  "title_text": "Relativization of symmetries on quandles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/748q46vapdxvj",
  "venue": "arXiv",
  "versions": []
}