Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

• 成果类型: Article; Early Access
• 署名作者: Isenrich, Claudio Llosa; Py, Pierre
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01223-3
• 发表日期: 2023
• 关键词: numbers; forms

摘要

We prove that in a cocompact complex hyperbolic arithmetic lattice Gamma < PU(m, 1) of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type Fm-1 but not of type F-m. This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer's conjecture for aspherical Kahler manifolds.