Vol. 295, No. 1, 2018

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ISSN: 0030-8730
Homomorphisms of fundamental groups of planar continua

Curtis Kent

Vol. 295 (2018), No. 1, 43–55
Abstract

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.

Keywords
Peano continuum, fundamental group, planar
Mathematical Subject Classification 2010
Primary: 20F34, 55P10, 57N05
Secondary: 54E45
Milestones
Received: 10 November 2015
Revised: 1 December 2017
Accepted: 5 December 2017
Published: 13 March 2018
Authors
Curtis Kent
Department of Mathematics
Brigham Young University
Provo, UT
United States