Rank gradient, cost of groups and the rank versus Heegaard genus problem

被引：44

作者：

Abert, Miklos ^{[1
]}

Nikolov, Nikolay ^{[2
]}

机构：

[1] Alfred Renyi Inst Math, H-1053 Budapest, Hungary

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2012年 / 14卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.4171/JEMS/344

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the 'rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the 'fixed price problem' in topological dynamics.

引用

页码：1657 / 1677

页数：21

共 32 条

[11]

Farber M, 1998, MATH ANN, V311, P335, DOI 10.1007/s002080050190

[12]

Gaboriau D, 2000, INVENT MATH, V139, P41, DOI 10.1007/s002229900019

[13]

Gaboriau D., 2002, Publ. Math. Inst. Hautes Etudes Sci., P93

[14]

GRIGORCHUK, 2000, Proc. Steklov Inst. Math., V231, P134