Faithful linear representations of the braid groups

Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque no. 276 (2002), Talk no. 878, p. 389-409

MR 1886767 | Zbl 1050.20026 | 1 citation in Numdam

@incollection{SB_1999-2000__42__389_0,
     author = {Turaev, Vladimir G.},
     title = {Faithful linear representations of the braid groups},
     booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {276},
     year = {2002},
     note = {talk:878},
     pages = {389-409},
     zbl = {1050.20026},
     mrnumber = {1886767},
     language = {en},
     url = {http://www.numdam.org/item/SB_1999-2000__42__389_0}
}

Turaev, Vladimir. Faithful linear representations of the braid groups, in Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Talk no. 878, pp. 389-409. http://www.numdam.org/item/SB_1999-2000__42__389_0/

References

[Bi1] S. Bigelow - The Burau representation is not faithful for $n \geq 5$ , Preprint math.GT/9904100.

[Bi2] S. Bigelow - Braid groups are linear, Preprint math. GR/0005038. | MR 1815219

[Bir] J. S. Birman - Braids, links, and mapping class groups, Ann. of Math. Stud., vol. 82, Princeton Univ. Press, Princeton, N.J., 1974. | MR 375281 | Zbl 0305.57013

[BW] J. S. Birman, H. Wenzl - Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313 (1989), 249-273. | MR 992598 | Zbl 0684.57004

[Br] R. Brauer - On algebras which are connected with the semisimple continuous groups, Ann. of Math. 38 (1937), 857-872. | MR 1503378 | Zbl 0017.39105

[Bu] W. Burau - Über Zopfgruppen und gleichsinnig verdrillte Verkettungen, Abh. Math. Semin. Hamburg. Univ. 11 (1935), 179-186. | Zbl 0011.17801

[Ch] R. Charney - Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995), 307-324. | MR 1314589 | Zbl 0813.20042

[DFG] J. L. Dyer, E. Formanek, E. K. Grossman - On the linearity of automorphism groups of free groups, Arch. Math. (Basel) 38 (1982), 404-409. | MR 666911 | Zbl 0476.20025

[FLP] A. Fathi, F. Laudenbach, V. Poenaru - Travaux de Thurston sur les surfaces, Astérisque 66-67 (1991), Soc. Math. France, Paris. | MR 1134426 | Zbl 0446.57010

[FP] E. Formanek, C. Procesi - The automorphism group of a free group is not linear, J. Algebra 149 (1992), 494-499. | MR 1172442 | Zbl 0780.20023

[Ga] F. A. Garside - The braid group and other groups, Quart. J. Math. Oxford 20 (1969), 235-254. | MR 248801 | Zbl 0194.03303

[Iv1] N. V. Ivanov - Automorphisms of Teichmüller modular groups, Topology and geometry - Rohlin Seminar, Lecture Notes in Math., vol. 1346, Springer, Berlin-New York (1988), 199-270. | MR 970079 | Zbl 0657.57004

[Iv2] N. V. Ivanov - Subgroups of Teichmüller modular groups, Transl. of Math. Monographs, vol. 115. Amer. Math. Soc., Providence, RI, 1992. | MR 1195787 | Zbl 0776.57001

[Jo] V. F. R. Jones - Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987), 335-388. | MR 908150 | Zbl 0631.57005

[Ka] C. Kassel - L'ordre de Dehornoy sur les tresses, Séminaire Bourbaki, exposé 865 (novembre 1999). This volume. | Numdam

[Kr1] D. Krammer - The braid group $B_{4}$ is linear, Preprint, Basel (1999). | MR 1804157

[Kr2] D. Krammer - Braid Groups are linear, Preprint, Basel (2000). | MR 1888796

[La] R. J. Lawrence - Homological representations of the Hecke algebra, Comm. Math. Phys. 135 (1990), 141-191. | MR 1086755 | Zbl 0716.20022

[LP] D. D. Long, M. Paton - The Burau representation is not faithful for $n \geq 6$ , Topology 32 (1993), 439-447. | Zbl 0810.57004

[Mi] J. Michel - A note on words in braid monoids, J. Algebra 215 (1999), 366- 377. | MR 1684142 | Zbl 0937.20017

[Mo] J. A. Moody - The Burau representation of the braid group $B_{n}$ is unfaithful for large $n$ , Bull. Amer. Math. Soc. (N.S.) 25 (1991), 379-384. | MR 1098347 | Zbl 0751.57005

[Mu] J. Murakami - The Kauffman polynomial of links and representation theory, Osaka J. Math. 24 (1987), 745-758. | MR 927059 | Zbl 0666.57006

[We] H. Wenzl - Quantum groups and subfactors of type $B, C$ , and $D$ , Comm. Math. Phys. 133 (1990), 383-432. | MR 1090432 | Zbl 0744.17021

[Zi] M. G. Zinno - On Krammer's Representation of the Braid Group, Preprint math.RT/0002136.