A combination theorem for special cube complexes

• 成果类型: Article
• 署名作者: Haglund, Frederic; Wise, Daniel T.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.3.2
• 发表日期: 2012
• 页码: 1427-1482
• 关键词: SUBGROUPS

摘要

We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex sub-groups of right-angled Artin groups. As a result we obtain, linearity and the separability of quasiconvex subgroups, for the groups we consider. Our result applies in particular to compact negatively curved cube complexes whose hyperplanes don't self-intersect. For cube complexes with word-hyperbolic fundamental group, we are able to show that they are virtually special if and only if the hyperplanes are separable. In a final application, we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special.