Braid groups are linear
| dc.creator | Krammer, Daan | |
| dc.date | 2004-05-11 | |
| dc.date.accessioned | 2026-07-07T05:08:08Z | |
| dc.date.available | 2026-07-07T05:08:08Z | |
| dc.description | In a previous work [11], the author considered a representation of the braid group ρ: B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be faithful for all n by a beautiful topological argument. The present paper gives a different proof of the faithfulness for all n. We establish a relation between the Charney length in the braid group and exponents of t. A certain B_n-invariant subset of the module is constructed whose properties resemble those of convex cones. We relate line segments in this set with the Thurston normal form of a braid. | |
| dc.description | 26 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0405198 | |
| dc.identifier | http://arxiv.org/abs/math/0405198 | |
| dc.identifier | Ann. of Math. (2), Vol. 155 (2002), no. 1, 131--156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71141 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.title | Braid groups are linear | |
| dc.type | text |