Vol. 295, No. 1, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Vol. 292: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
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