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Braid groups are linear

Author(s): Stephen J. Bigelow
Journal: J. Amer. Math. Soc. 14 (2001), 471-486.
MSC (2000): Primary 20F36; Secondary 57M07, 20C15
Posted: December 13, 2000
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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: 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
Posted: December 13, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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