Fundamental groups of one-dimensional spaces

• Autorzy: Gerhard Dorfer , Jörg M. Thuswaldner , Reinhard Winkler
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A80: Fractals
• 14F35: Homotopy theory; fundamental groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 2
• Strony: 137-169

Daty

wydano

2013

Twórcy

autor

Gerhard Dorfer

• Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria

autor

Jörg M. Thuswaldner

• Chair of Mathematics and Statistics, Department of Mathematics, and Information Technology, University of Leoben, Franz-Josef-Straße 18, 8700 Leoben, Austria

autor

Reinhard Winkler

• Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria

Identyfikatory

DOI

10.4064/fm223-2-2