On the structure of the commutator subgroup of certain homeomorphism groups

被引：3

作者：

Michalik, Ilona ^{[1
]}

Rybicki, Tomasz ^{[1
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2011年 / 158卷 / 11期

关键词：

Group of homeomorphisms; Factorizable group; Commutator subgroup; Perfectness; Uniform perfectness; Simplicity; Uniform simplicity; Open manifold; LIPSCHITZ HOMEOMORPHISMS; DIFFEOMORPHISMS; FOLIATION; PERFECT;

D O I：

10.1016/j.topol.2011.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An important theorem of Ling states that if G is any factorizable non-fixing group of homeomorphisms of a paracompact space then its commutator subgroup [G, G] is perfect. This paper is devoted to further studies on the algebraic structure (e.g. uniform perfectness, uniform simplicity) of [G, G] and [(G) over tilde, (G) over tilde], where (G) over tilde is the universal covering group of G. In particular, we prove that if G is a bounded factorizable non-fixing group of homeomorphisms then [G, G] is uniformly perfect (Corollary 3.4). The case of open manifolds is also investigated. Examples of homeomorphism groups illustrating the results are given. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1314 / 1324

页数：11

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