Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 1 min ago
PreprintCC BY 4.0arXiv

The Burau representation of the braid group is faithful for n = 4

  • Vasudha Bharathram
  • Joan S. Birman
  • Tara E. Brendle
Open at sourcePDFDOICite

Abstract

In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.

Related

  1. Representations of the modular group of the twice-punctured torus and Burau representations
    Elisha Falbel, Grace Garden, Antonin Guilloux
    HALPreprintCC BY-NC-ND 4.0Full textGeometry & topologyHAL
  2. A faithful representation and profinite completion
    Wonyong Jang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  3. A Faithful Action of the Mapping Class Group Mod(Sg) on the (2g−1)-Sphere
    Shile Wang
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. A virtual geometric action of a braid group
    Sylvain Barré, Mikaël Pichot
    Beiträge zur Algebra und Geometrie = Contributions to Algebra and GeometryPreprintCC BY 4.0Full textGeneral mathematicsHAL
  5. Distinguished bases and the braid group action for solutions of the tt*-Toda equations
    Yudai Hateruma
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{bharathram2026burau,
  title = {{The Burau representation of the braid group is faithful for n = 4}},
  author = {Vasudha Bharathram and Joan S. Birman and Tara E. Brendle},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.05283},
  eprint = {2607.05283},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.05283},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Burau representation of the braid group is faithful for n = 4
AU  - Vasudha Bharathram
AU  - Joan S. Birman
AU  - Tara E. Brendle
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2607.05283
UR  - https://arxiv.org/abs/2607.05283
AB  - In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.
ER  -