Glasnik Matematicki, Vol. 46, No. 2 (2011), 505-511.

AN ALTERNATE PROOF THAT THE FUNDAMENTAL GROUP OF A PEANO CONTINUUM IS FINITELY PRESENTED IF THE GROUP IS COUNTABLE

J. Dydak and Ž. Virk

University of Tennessee, Knoxville, TN 37996, USA
e-mail: dydak@math.utk.edu
e-mail: zigavirk@gmail.com


Abstract.   We give an alternate proof, using coarse geometry, that if the fundamental group of a compact, connected, locally connected metric space is countable, then the fundamental group is finitely presented. This result was first proved by Katsuya Eda and the argument can be found in [5].

2000 Mathematics Subject Classification.   55Q52, 20F65, 14F35.

Key words and phrases.   Coarse geometry, coarse connectivity, finitely presented groups, fundamental group, locally connected compact metric spaces.


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DOI: 10.3336/gm.46.2.18


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