Image of the Burau representation at d-th roots of unity

Type: Article

Publication Date: 2014-02-20

Citations: 24

DOI: https://doi.org/10.4007/annals.2014.179.3.4

Abstract

We prove that the image of the Full braid group $B_{n+1}$ on $n+1$ strands under the Burau representation, evaluated at a primitive $d$-th root of unity is arithmetic provided $n\geq d$.

Locations

  • arXiv (Cornell University) - View - PDF
  • DataCite API - View
  • Annals of Mathematics - View - PDF

Similar Works

Action Title Year Authors
+ Full Braid Group at Roots of Unity 2012 T. N. Venkataramana
+ Honors Thesis on the faithfulness of the Burau representation at roots of unity 2017 Thomas Chuna
+ Honors Thesis: On the faithfulness of the Burau representation at roots of unity 2017 Thomas Chuna
+ The Burau representation of the Braid group 2020 Raquel Revilla Bouso
+ PDF Chat Attacks on the Faithfulness of the Burau Representation of the Braid Group $B_4$ 2016 Mohammad Y. Chreif
Mohammad N. Abdulrahim
+ PDF Chat On Burau representations at roots of unity 2014 Louis Funar
Toshitake Kohno
+ PDF Chat On the Burau representation of $B_3$ modulo $p$ 2024 Donsung Lee
+ The Burau representation of the braid group and the Nielsen-Thurston classification 1993 Takashi Matsuoka
+ PDF Chat On Burau representations at roots of unity 2014 Louis Funar
Toshitake Kohno
+ On the Burau representation of the braid group $B_4$ 2020 Amitesh Datta
+ A new $n$ dimensional representation of Artin braid group $B_n$, and a general Burau representation 2018 Arash Pourkia
+ Forks, noodles and the Burau representation for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml41" display="inline" overflow="scroll" altimg="si41.gif"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> 2018 Anzor Beridze
P. Traczyk
+ PDF Chat Observed Periodicity Related to the Four-Strand Burau Representation 2017 Neil J. Fullarton
Richard Shadrach
+ A new $n$ dimensional representation of Artin braid group $B_n$ 2018 Arash Pourkia
+ The Burau representation of the braid group is pairwise free 1979 N. Smythe
+ PDF Chat A Garside-theoretic analysis of the Burau representations 2017 Matthieu Calvez
Tetsuya Ito
+ Characterizing the kernel of the Burau representation modulo 2 for the 4-strand braid group 2023 Donsung Lee
+ PDF Chat Generators for the level $m$ congruence subgroups of braid groups 2024 Ishan Banerjee
Peter Huxford
+ Garside-theoretic analysis of Burau representations 2014 Matthieu Calvez
Tetsuya Ito
+ Observed periodicity related to the four-strand Burau representation 2016 Neil J. Fullarton
Richard Shadrach