Homomorphisms of fundamental groups of planar continua

Curtis Kent

Vol. 295 (2018), No. 1, 43–55

DOI: 10.2140/pjm.2018.295.43

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