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2021 On the Burau representation of $B_4$
Vasudha Bharathram, Joan Birman
Involve 14(1): 143-154 (2021). DOI: 10.2140/involve.2021.14.143

Abstract

In 1936 W. Burau discovered an interesting family of n×n matrices that give a linear representation of Artin’s classical braid group Bn, n=1,2,. A natural question followed very quickly: is the so-called Burau representation faithful? Over the years it was proved to be faithful for n3, nonfaithful for n5, but the case of n=4 remains open to this day, in spite of many papers on the topic. This paper introduces braid groups, describes the problem in ways that make it accessible to readers with a minimal background, reviews the literature, and makes a contribution that reinforces conjectures that the Burau representation of B4 is faithful.

Citation

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Vasudha Bharathram. Joan Birman. "On the Burau representation of $B_4$." Involve 14 (1) 143 - 154, 2021. https://doi.org/10.2140/involve.2021.14.143

Information

Received: 17 July 2020; Revised: 1 October 2020; Accepted: 24 October 2020; Published: 2021
First available in Project Euclid: 22 April 2021

Digital Object Identifier: 10.2140/involve.2021.14.143

Subjects:
Primary: 20F36
Secondary: 20C99 , 20E05

Keywords: Braid group , Burau representation , free group , Heisenberg group , Klein 4-group

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 1 • 2021
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