{
  "abstract": "We study webs on surfaces for the $\\rm{PGL}_2$ skein theory specialized at roots of unity. We construct the $\\rm{PGL}_2$ analogue of Chebyshev polynomials and use them to construct central elements in the skein algebra. We then focus on the cases of the 3-punctured sphere and the closed torus. We compute the Frobenius homomorphism for these two surfaces and show that the $\\rm{PGL}_2$ Frobenius homomorphism for the torus is not injective when the quantum parameter $q^2$ is a root of unity of even order $n.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01881",
  "author_total": 6,
  "authors": [
    {
      "name": "Vijay Higgins"
    },
    {
      "name": "Bryan Silva"
    },
    {
      "name": "Amy Somers"
    },
    {
      "name": "David Stephens"
    },
    {
      "name": "Srijan Sundar"
    },
    {
      "name": "Parth Wokhlu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kvb8g95yj2ch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01881",
  "fulltext_url": null,
  "id": "1kvb8g95yj2ch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01881",
  "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": "W7216043221",
  "pdf_url": "https://arxiv.org/pdf/2610.01881",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kvb8g95yj2ch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01881",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01881"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$\\rm{PGL}_2$ webs at roots of unity",
  "title_text": "PGL_2 webs at roots of unity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/1kvb8g95yj2ch",
  "venue": "arXiv",
  "versions": []
}