Download this article
 Download this article For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
The Griffiths double cone group is isomorphic to the triple

Samuel M. Corson

Vol. 327 (2023), No. 2, 297–336
Abstract

It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if κ is a cardinal such that 2 κ 20 then the κ-fold cone has the same fundamental group as the double cone. The isomorphisms produced are nonconstructive, and no isomorphism between the fundamental group of the 2- and of the κ-fold cones, with 2 < κ, can be realized via continuous mappings.

Keywords
fundamental group, Griffiths space, Hawaiian earring, topological cone
Mathematical Subject Classification
Primary: 03E75, 20A15, 55Q52
Secondary: 20F10, 20F34
Milestones
Received: 29 April 2021
Revised: 19 January 2024
Accepted: 19 January 2024
Published: 12 March 2024
Authors
Samuel M. Corson
School of Mathematics
Universidad del País Vasco
Leioa
Spain

Open Access made possible by participating institutions via Subscribe to Open.