{
  "abstract": "It is a well-known result of Gustafson, Halmos and Radjavi, dating back to 1976, that any matrix $A$ in $SL_n(\\mathbb{C})$ is a product of at most 4 involutions. We consider a natural continuous and holomorphic parameter dependence of this result in the spirit of Vaserstein and Gromov. Our main result shows that null-homotopy characterizes exactly those matrices in the special linear group over rings of continuous or holomorphic functions that are finite products of involutions. We give an upper bound $I(n, d)$, depending only on the size $n$ of the matrices and the dimension $d$ of the parameter space, for the number of involutions needed in the factorization. Our upper bound is not optimal, however we show that for fixed $n$ the optimal upper bound tends to infinity as $d\\to \\infty$. In some cases we are able to determine the optimal bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26808",
  "author_total": 4,
  "authors": [
    {
      "name": "Gaofeng Huang"
    },
    {
      "name": "Frank Kutzschebauch"
    },
    {
      "name": "Tran Nam Son"
    },
    {
      "name": "Truong Huu Dung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0q9n5cnzzt51j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26808",
  "fulltext_url": null,
  "id": "0q9n5cnzzt51j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26808",
  "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.CV"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7214148919",
  "pdf_url": "https://arxiv.org/pdf/2609.26808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0q9n5cnzzt51j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Parametric decompositions into products of involutions",
  "title_text": "Parametric decompositions into products of involutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0q9n5cnzzt51j",
  "venue": "arXiv",
  "versions": []
}