Fundamental groups having the whole information of spaces
type: Item
instance of: scholarly article
title: Fundamental groups having the whole information of spaces
zbMATH Open document ID: 1063.55011
author: Greg Conner
author: Katsuya Eda
published in: Topology and its Applications
publication date: 2005-02-22T00:00:00Z
review text: The authors propose a new construction of a space from a group, and show that applying this construction to the fundamental group of certain spaces produces the original spaces, which implies that the fundamental group of such spaces has the same information as the topological space itself. Their construction uses homomorphic images of the fundamental group of the Hawaiian earring, and is based on a previous result: ``One-dimensional, locally path-connected, path connected, metric spaces which are not semi-locally simply connected at any point, and have isomorphic fundamental groups, are homeomorphic'' [see \textit{K. Eda}, ibid. 123, No. 3, 479--505 (2002; Zbl 1032.55013)]. According to this, the topologies of one-dimensional fractals which are Peano continua and have nontrivial fundamental groups, i.e., the Sierpinski gasket, the Sierpinski carpet and the Menger sponge, are recovered from their fundamental groups. Finite or countable products of such spaces are also recovered from their fundamental groups.
Mathematics Subject Classification ID: 55Q99
Mathematics Subject Classification ID: 55Q20
Mathematics Subject Classification ID: 55Q70
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 55M05
zbMATH DE Number: 2136473
zbMATH Keywords: fundamental group
zbMATH Keywords: Hawaiian earring
reviewed by: J. Remedios
MaRDI profile type: Publication
full work available at URL: j.topol.2003.05.005
OpenAlex ID: W1979081712
cites work: The combinatorial structure of the Hawaiian earring group
cites work: Free \(\sigma\)-products and noncommutatively slender groups
cites work: Free \(\sigma\)-products and fundamental groups of subspaces of the plane
cites work: The Singular Homology of the Hawaiian Earring
cites work: Infinite Products of Semi-Groups and Local Connectivity
cites work: Q3253828
cites work: Q3270631
cites work: A Van Kampen Theorem for Weak Joins
DOI: 10.1016/J.TOPOL.2003.05.005
description: scientific article; zbMATH DE number 2136473