Niveau: Supérieur, Doctorat, Bac+8
On Burau's representations at roots of unity Louis Funar Toshitake Kohno Institut Fourier BP 74, UMR 5582 IPMU, Graduate School of Mathematical Sciences University of Grenoble I The University of Tokyo 38402 Saint-Martin-d'Heres cedex, France 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914 Japan e-mail: e-mail: May 10, 2012 Abstract We consider subgroups of the braid groups which are generated by n-th powers of the stan- dard generators and prove that any infinite intersection (with even n) is trivial. This is mo- tivated by some conjectures of Squier concerning the kernels of Burau's representations of the braid groups at roots of unity. Furthermore, we show that the image of the braid group on 3 strands by these representations is either a finite group, for a few roots of unity, or a finite extension of a triangle group, by using geometric methods. 2000 MSC Classification: 57 M 07, 20 F 36, 20 F 38, 57 N 05. Keywords: Mapping class group, Dehn twist, Temperley-Lieb algebra, triangle group, braid group, Burau representation. 1 Introduction and statements The first part of the present paper is devoted to the study of groups related to the kernels of Burau's representations of the braid groups at roots of unity.
- infinite order
- group
- over any infinite
- burau's representations
- then completely
- reducible only when
- braid relation
- c?-algebra structure
- temperley-lieb algebra