The Burau representation of the braid group 𝐵_{𝑛} is unfaithful for large 𝑛

Moody, John Atwell

doi:10.1090/S0273-0979-1991-16080-5

The Burau representation of the braid group $B_n$ is unfaithful for large $n$
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by John Atwell Moody PDF

Bull. Amer. Math. Soc. 25 (1991), 379-384

References

J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), no. 2, 275–306. MR 1501429, DOI 10.1090/S0002-9947-1928-1501429-1
Wilhelm Magnus, Collected papers, Springer-Verlag, New York, 1984. Edited and with introductory material by Gilbert Baumslag and Bruce Chandler. MR 725504
Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, DOI 10.2307/1971403
D. D. Long, On the linear representation of braid groups, Trans. Amer. Math. Soc. 311 (1989), no. 2, 535–560. MR 943606, DOI 10.1090/S0002-9947-1989-0943606-3
Edward Witten, Quantum field theory and the Jones polynomial, Braid group, knot theory and statistical mechanics, Adv. Ser. Math. Phys., vol. 9, World Sci. Publ., Teaneck, NJ, 1989, pp. 239–329. MR 1062429, DOI 10.1142/9789812798350_{0}009
Toshitake Kohno, Linear representations of braid groups and classical Yang-Baxter equations, Braids (Santa Cruz, CA, 1986) Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 339–363. MR 975088, DOI 10.1090/conm/078/975088
D. D. Long, A note on the normal subgroups of mapping class groups, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 1, 79–87. MR 809501, DOI 10.1017/S0305004100063957