On the fundamental groups of one-dimensional spaces

被引：59

作者：

Cannon, J. W. ^{[1
]}

Conner, G. R. ^{[1
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2006年 / 153卷 / 14期

基金：

美国国家科学基金会;

关键词：

homotopically Hausdorff; one-dimensional; fundamental group; dendrite; homology; shape injective; extended commutator subgroup; rich abelianization; 2-set simple cover; reduced path; infinite multiplication;

D O I：

10.1016/j.topol.2005.10.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study here a number of questions raised by examining the fundamental groups of complicated one-dimensional spaces. The first half of the paper considers one-dimensional spaces as such. The second half proves related results for general spaces that are needed in the first half but have independent interest. Among the results we prove are the theorem that the fundamental group of a separable, connected, locally path connected, one-dimensional metric space is free if and only if it is countable if and only if the space has a universal cover and the theorem that the fundamental group of a compact, one-dimensional, connected metric space embeds in an inverse limit of finitely generated free groups and is shape injective. (C) 2005 Elsevier B.V. All rights reserved.

引用

页码：2648 / 2672

页数：25

共 17 条

[1]

BOGLEY WA, WEIGHTED COMBINATORI

[2]

Cannon J.W., 2002, HDB GEOMETRIC TOPOLO, P261

[3] The combinatorial structure of the Hawaiian earring group [J].