Fundamental groups of one-dimensional spaces

Gerhard Dorfer, Jörg M. Thuswaldner, and Reinhard Winkler. "Fundamental groups of one-dimensional spaces." Fundamenta Mathematicae 223.2 (2013): 137-169. <http://eudml.org/doc/283223>.

@article{GerhardDorfer2013,
abstract = {Let X be a metrizable one-dimensional continuum. We describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from the fundamental group of the Hawaiian earring to that of X.},
author = {Gerhard Dorfer, Jörg M. Thuswaldner, Reinhard Winkler},
journal = {Fundamenta Mathematicae},
keywords = {one-dimensional space; fundamental group},
language = {eng},
number = {2},
pages = {137-169},
title = {Fundamental groups of one-dimensional spaces},
url = {http://eudml.org/doc/283223},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Gerhard Dorfer
AU - Jörg M. Thuswaldner
AU - Reinhard Winkler
TI - Fundamental groups of one-dimensional spaces
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 2
SP - 137
EP - 169
AB - Let X be a metrizable one-dimensional continuum. We describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from the fundamental group of the Hawaiian earring to that of X.
LA - eng
KW - one-dimensional space; fundamental group
UR - http://eudml.org/doc/283223
ER -