{
  "abstract": "We study representations from the pure mapping class group of the twice-punctured torus PMod(S_{1,2}) to SL(3, C) with a particular focus on those coming from the reduced Burau representations. We exploit connections between PMod(S_{1,2}), the braid group on four strands B_4 , and the fundamental group of the once-punctured torus π_1(S_{1,1}) to review and reprove results in multiple directions, including: a uniqueness result for extensions from irreducible representations on π_1(S_{1,1}) to PMod(S_{1,2}), a classification of representations from PMod(S_{1,2}) to SL(3, C), and a survey on specific parameters for Burau representations with geometric meaning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Elisha Falbel"
    },
    {
      "name": "Grace Garden"
    },
    {
      "name": "Antonin Guilloux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhpdhhy82rmfx.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "dhpdhhy82rmfx",
  "issns": [],
  "landing_url": "https://hal.sorbonne-universite.fr/hal-05839040v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-gt"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.sorbonne-universite.fr/hal-05839040/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhpdhhy82rmfx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05839040",
      "source": "hal",
      "url": "https://hal.sorbonne-universite.fr/hal-05839040v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-gt",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Representations of the modular group of the twice-punctured torus and Burau representations",
  "title_text": "Representations of the modular group of the twice-punctured torus and Burau representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/dhpdhhy82rmfx",
  "venue": "HAL",
  "versions": []
}