Observed Periodicity Related to the Four-Strand Burau Representation

DOI10.1080/10586458.2017.1335625zbMath1470.20014arXiv1610.04648OpenAlexW2535801315MaRDI QIDQ5743085

Richard Shadrach, Neil J. Fullarton

Publication date: 8 May 2019

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04648

zbMATH Keywords

Burau representationbraid groupgeometric group theory

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Geometric group theory (20F65) Braid groups; Artin groups (20F36)

Cites Work

• The Burau representation is not faithful for \(n=5\)
• A kernel of a braid group representation yields a knot with trivial knot polynomials
• The Burau representation is not faithful for \(n\geq 6\)
• The Burau representation of the braid group 𝐵_{𝑛} is unfaithful for large 𝑛
• DOES THE JONES POLYNOMIAL DETECT THE UNKNOT?

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