ISOPERIMETRIC INEQUALITIES FOR POINCARE DUALITY GROUPS

被引：1

作者：

Kielak, Dawid ^{[1
]}

Kropholler, Peter ^{[2
]}

机构：

[1] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[2] Univ Southampton, Math Sci, Southampton SO17 1BJ, Hants, England

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 11期

基金：

欧洲研究理事会;

关键词：

CONVERGENCE GROUPS; INFINITE INDEX; SUBGROUPS;

D O I：

10.1090/proc/15596

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that every oriented n-dimensional Poincare duality group over a *-ring R is amenable or satisfies a linear homological isoperimetric inequality in dimension n - 1. As an application, we prove the Tits alternative for such groups when n = 2. We then deduce a new proof of the fact that when n = 2 and R = Z then the group in question is a surface group.

引用

页码：4685 / 4698

页数：14

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