Braid groups are linear

• 成果类型: Article
• 署名作者: Krammer, D
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062152
• 发表日期: 2002
• 页码: 131-156
• 关键词: representation; Algebra

摘要

In a previous work [11], the author considered a representation of the braid group rho: B-n - GL(m)(Z[q(+/-1), t(+/-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.