A+ CATEGORY SCIENTIFIC UNIT

Fundamental groups of one-dimensional spaces

Volume 223 / 2013

Gerhard Dorfer, Jörg M. Thuswaldner, Reinhard Winkler Fundamenta Mathematicae 223 (2013), 137-169 MSC: Primary 14F35; Secondary 28A80. DOI: 10.4064/fm223-2-2

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 $X$.

Authors

  • Gerhard DorferInstitute of Discrete Mathematics and Geometry
    Vienna University of Technology
    Wiedner Hauptstr. 8-10/104
    1040 Wien, Austria
    e-mail
  • Jörg M. ThuswaldnerChair of Mathematics and Statistics
    Department of Mathematics
    and Information Technology
    University of Leoben
    Franz-Josef-Straße 18
    8700 Leoben, Austria
    e-mail
  • Reinhard WinklerInstitute of Discrete Mathematics and Geometry
    Vienna University of Technology
    Wiedner Hauptstr. 8-10/104
    1040 Vienna, Austria
    e-mail

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