Faithful linear representations of the braid groups

Turaev, Vladimir

Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 878, 21 p.

MR Zbl | 2 citations dans Numdam

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

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Turaev, Vladimir. Faithful linear representations of the braid groups, dans Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 878, 21 p.. https://www.numdam.org/item/SB_1999-2000__42__389_0/

Bibliographie
Cité par

[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

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

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

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

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

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

[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. | Zbl | MR

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

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

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

[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. | Zbl | MR

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

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

[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

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

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

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

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

[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. | Zbl | MR

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

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

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