The Griffiths double cone group is isomorphic to the triple

Samuel M. Corson

Vol. 327 (2023), No. 2, 297–336

DOI: 10.2140/pjm.2023.327.297

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 $\kappa$ is a cardinal such that $2\le \kappa \le 2^{{\aleph }_0}$ then the $\kappa$-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 $\kappa$-fold cones, with $2<\kappa$, 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