Geodesic
Braid groups are linear
Bigelow, Stephen1
1Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052
Journal of the American Mathematical Society, Tome 14 (2001) no. 2, pp. 471-486

Voir la notice de l'article provenant de la source American Mathematical Society

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 $n$.
DOI : 10.1090/S0894-0347-00-00361-1

Bigelow, Stephen  1

1 Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052 
Bigelow, Stephen. Braid groups are linear. Journal of the American Mathematical Society, Tome 14 (2001) no. 2, pp. 471-486. doi: 10.1090/S0894-0347-00-00361-1
@article{10_1090_S0894_0347_00_00361_1,
     author = {Bigelow, Stephen},
     title = {Braid groups are linear},
     journal = {Journal of the American Mathematical Society},
     pages = {471--486},
     year = {2001},
     volume = {14},
     number = {2},
     doi = {10.1090/S0894-0347-00-00361-1},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00361-1/}
}
TY  - JOUR
AU  - Bigelow, Stephen
TI  - Braid groups are linear
JO  - Journal of the American Mathematical Society
PY  - 2001
SP  - 471
EP  - 486
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00361-1/
DO  - 10.1090/S0894-0347-00-00361-1
ID  - 10_1090_S0894_0347_00_00361_1
ER  - 
%0 Journal Article
%A Bigelow, Stephen
%T Braid groups are linear
%J Journal of the American Mathematical Society
%D 2001
%P 471-486
%V 14
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00361-1/
%R 10.1090/S0894-0347-00-00361-1
%F 10_1090_S0894_0347_00_00361_1

[1] Robertson, M. S. The variation of the sign of 𝑉 for an analytic function 𝑈+𝑖𝑉 Duke Math. J. 1939 512 519

[2] Birman, Joan S., Wenzl, Hans Braids, link polynomials and a new algebra Trans. Amer. Math. Soc. 1989 249 273

[3] Travaux de Thurston sur les surfaces 1979 284

[4] Lawrence, R. J. Homological representations of the Hecke algebra Comm. Math. Phys. 1990 141 191

[5] Long, D. D., Paton, M. The Burau representation is not faithful for 𝑛≥6 Topology 1993 439 447

[6] Moody, John Atwell The Burau representation of the braid group 𝐵_{𝑛} is unfaithful for large 𝑛 Bull. Amer. Math. Soc. (N.S.) 1991 379 384

[7] Murakami, Jun The Kauffman polynomial of links and representation theory Osaka J. Math. 1987 745 758

[8] Paris, L., Rolfsen, D. Geometric subgroups of surface braid groups Ann. Inst. Fourier (Grenoble) 1999 417 472

Cité par Sources :