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Abstract
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We prove that every homomorphism from the fundamental group of a planar Peano
continuum to the fundamental group of a planar or one-dimensional Peano continuum
is induced by a continuous map up to conjugation. This is used to provide an
uncountable family of planar Peano continua with pairwise nonisomorphic
fundamental groups each of which is not homotopy equivalent to a one-dimensional
space.
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Keywords
Peano continuum, fundamental group, planar
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Mathematical Subject Classification 2010
Primary: 20F34, 55P10, 57N05
Secondary: 54E45
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Milestones
Received: 10 November 2015
Revised: 1 December 2017
Accepted: 5 December 2017
Published: 13 March 2018
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