Image of the Burau representation at d-th roots of unity

• 成果类型: Article
• 署名作者: Venkataramana, T. N.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.179.3.4
• 发表日期: 2014
• 页码: 1041-1083
• 关键词: arithmetic subgroups; Generators

摘要

We show that the image of the braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree d. This is deduced by proving the arithmeticity of the image of the braid group on n+1 letters under the Burau representation evaluated at d-th roots of unity when n >= 2d.