Special cubulation of strict hyperbolization

• 成果类型: Article; Early Access
• 署名作者: Lafont, Jean-Francois; Ruffoni, Lorenzo
• 署名单位: University System of Ohio; Ohio State University; Tufts University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01241-9
• 发表日期: 2024
• 关键词: aspherical manifolds; conjecture; FINITENESS; SUBGROUPS; PROPERTY; lattices; SPACES; trees

摘要

We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence linear and residually finite. Our strategy consists in constructing an action of a hyperbolized group on a certain dual CAT ( 0 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\operatorname {CAT}(0)$\end{document} cubical complex. As a result, all the common applications of strict hyperbolization are shown to provide manifolds with virtually compact special fundamental group. In particular, we obtain examples of closed negatively curved Riemannian manifolds whose fundamental groups are linear and virtually algebraically fiber.