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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Braid groups are linear


Author: Stephen J. Bigelow
Journal: J. Amer. Math. Soc. 14 (2001), 471-486
MSC (2000): Primary 20F36; Secondary 57M07, 20C15
Published electronically: December 13, 2000
MathSciNet review: 1815219
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Abstract:

The braid group $B_n$ can be defined as the mapping class group of the $n$-punctured disk. A group is said to be linear if it admits a faithful representation into a group of matrices over $\mathbf R$. Recently Daan Krammer has shown that a certain representation of the braid groups is faithful for the case $n=4$. In this paper, we show that it is faithful for all $n$.


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Additional Information

Stephen J. Bigelow
Affiliation: Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052
Email: bigelow@unimelb.edu.au

DOI: http://dx.doi.org/10.1090/S0894-0347-00-00361-1
PII: S 0894-0347(00)00361-1
Keywords: Braid group, linear, representation
Received by editor(s): May 11, 2000
Received by editor(s) in revised form: October 30, 2000
Published electronically: December 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society