Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

被引：2

作者：

Isenrich, Claudio Llosa ^{[1
]}

Py, Pierre ^{[2
,3
,4
,5
]}

机构：

[1] Karlsruhe Inst Technol, Fac Math, D-76131 Karlsruhe, Germany

[2] Univ Strasbourg, IRMA, F-67084 Strasbourg, France

[3] CNRS, F-67084 Strasbourg, France

[4] Univ Grenoble Alpes, Inst Fourier, F-38000 Grenoble, France

[5] CNRS, F-38000 Grenoble, France

来源：

INVENTIONES MATHEMATICAE | 2023年 / 235卷 / 1期

关键词：

NUMBERS; FORMS;

D O I：

10.1007/s00222-023-01223-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：233 / 254

页数：22