nLab Burau representation

Idea

A braid group representation.

Related concepts

• Alexander polynomial

References

The original article:

• Werner Burau, Über Zopfgruppen und gleichsinnig verdrillte Verkettungen, Abh. Math. Semin. Univ. Hambg. 11 (1935) 179–186 $[$doi:10.1007/BF02940722$]$

Review in the context of topological quantum computation:

• Colleen Delaney, Eric C. Rowell, Zhenghan Wang, Section 2 of: Local unitary representations of the braid group and their applications to quantum computing, Revista Colombiana de Matemáticas 50 2 (2017) 211 $[$arXiv:1604.06429, doi:10.15446/recolma.v50n2.62211$]$

See also:

• Wikipedia, Burau representation

Discussion in relation to configuration spaces of points, group completion and topological quantum field theory:

• Jack Morava, Dale Rolfsen: Toward the group completion of the Burau representation, Trans. Amer. Math. Soc. 376 (2023) 1845-1865 [arXiv:1809.01994, doi:10.1090/tran/8796]

See also:

• Vasudha Bharathram, Joan S. Birman, Tara E. Brendle: The Burau representation of the braid group is faithful for $n = 4$ [arXiv:2607.05283]