Braid groups are linear
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- by Stephen J. Bigelow
- J. Amer. Math. Soc. 14 (2001), 471-486
- DOI: https://doi.org/10.1090/S0894-0347-00-00361-1
- Published electronically: 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 $n$.References
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Bibliographic Information
- Stephen J. Bigelow
- Affiliation: Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052
- Email: bigelow@unimelb.edu.au
- Received by editor(s): May 11, 2000
- Received by editor(s) in revised form: October 30, 2000
- Published electronically: December 13, 2000
- © Copyright 2000 American Mathematical Society
- Journal: J. Amer. Math. Soc. 14 (2001), 471-486
- MSC (2000): Primary 20F36; Secondary 57M07, 20C15
- DOI: https://doi.org/10.1090/S0894-0347-00-00361-1
- MathSciNet review: 1815219